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Soybean meal is N_00 protein; cornmeal is N_01 protein. How many pounds of each should be mixed together in order to get a N_02 -pound mixture that is N_03 protein? | N_00 * v0 + N_01* v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 200.0 120.0 | 0.16 0.08 320.0 0.13 |
A car rented for N_00 dollars per day plus N_01 dollars per mile. Julia paid N_02 dollars for a N_03 -day rental. How far did she drive in miles? | N_01 * v0 = N_02 - N_00 | 214.0 | 29.0 0.08 46.12 1.0 |
A theater sold N_00 tickets to a play. Floor seats cost N_01 dollars each and balcony seats N_02 dollars each. Total receipts were N_03 dollars. How many floor seats were sold? How many balcony seats were sold? | N_01 * v0 + N_02 * v1 = N_03<BRG> v0 + v1 = N_00 | 390.0 510.0 | 900.0 12.0 10.0 9780.0 |
The sum of N_00 and a number is N_01 . | v0 = N_01 - N_00 | 10.0 | 20.0 30.0 |
You have space in your garden for N_00 small flowering bulbs. Crocus bulbs cost N_01 dollars each, and daffodil bulbs cost N_02 dollars each. Your budget allows you to spend N_03 dollars on bulbs. How many crocus bulbs and daffodil bulbs can you buy? | N_02 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_00 | 22.0 33.0 | 55.0 0.35 0.65 29.15 |
In a test of N_00 questions, N_01 points are given for each correct answer, and N_02 points are deducted for each one answered incorrectly. If Maria answered all of the questions and got a score of N_03 , how many did she get correct? | N_01 * v0 - N_02 * v1 = N_03 <BRG> v1 + v0 = N_00 | 19.0 11.0 | 30.0 20.0 5.0 325.0 |
Mario has N_00 pence to invest and decides to invest part of it at N_02 and the rest of it at N_03 . If the total interest for the year is N_01 pence, how much does Mario has to invest at N_02 rate, and how much does she have to invest at N_03 rate? | N_02 * v0 +N_03* v1 = N_01 <BRG> v1 + v0 = N_00 | 3200.0 1800.0 | 5000.0 245.0 0.04 0.065 |
N_00 teachers are going to a conference for a few days. Mrs. Jerrerson plans on spending N_01 dollars on N_02 meals and N_03 nights in a hotel. Mrs. Lloyd plans on spending N_04 dollars on N_05 meals and N_06 nights in a hotel. How much are they planning on spending per meal and per night for a hotel? | N_02 * v0 + N_03 * v1 = N_01 <BRG> N_05 * v0 + N_06 * v1 = N_04 | 13.0 80.0 | 2.0 502.0 14.0 4.0 370.0 10.0 3.0 |
Steve purchased tickets to a circus for N_00 adults and N_01 children. The total cost was N_02 dollars. The cost of a child's ticket was N_03 dollars less than the cost of an adult's ticket. Find the price of an adult ticket and a child's ticket. | N_00 * v0 + N_01 * v1 = N_02 <BRG> v0 - v1 = N_03 | 20.0 16.0 | 7.0 2.0 172.0 4.0 |
A chemist has a solution that is N_02 alcohol and one that is N_03 alcohol. He wants to make N_00 liters of a N_01 solution. How many liters of the N_02 solution should he add? How many liters of the N_03 solution should he add? | N_02* v0 + N_03 * v1 = N_00 * N_01 <BRG> v0 + v1 = N_00 | 50.0 30.0 | 80.0 0.3 0.18 0.5 |
You make candles and sell them for N_00 dollars each. The material to make up to N_01 candles costs N_01 dollars. How many candles must you sell to have a profit of N_02 dollars? | N_00 * v0 = N_01 + N_02 | 7.0 | 15.0 20.0 85.0 |
Junior's boat will go N_00 miles per hour in still water. If he can go N_01 miles downstream in the same amount of time as it takes to go N_02 miles upstream, then what is the speed of the current? | N_02 * v0 + N_01 * v0 = N_01 * N_00 - N_02 * N_00 | 2.14285714286 | 15.0 12.0 9.0 |
A factory makes three-legged stools and four-legged stools. They use the same kind of seats and legs for each. The only difference is the number of holes they bore in the seats for the legs. The company has N_00 seats and N_01 legs. | 3.0 * v0 + 4.0 * v1 = N_01 <BRG> v0 + v1 = N_00 | 83.0 78.0 | 161.0 566.0 |
A bank offers two checking plans. The Anywhere plan charges N_00 cents per check. The Accucheck plan costs $ N_01 a month, plus N_02 cents per check. For what number of checks will the Accucheck plan cost less than the Anywhere plan? | 0.01 * N_00 * v0 - 0.01 * N_02 * v0 = N_01 | 14.0 | 30.0 1.12 22.0 |
The student-teacher ratio for Washington High was reported to be N_00 to N_01 . If there are N_02 teachers, then how many students are there? | N_01 * v0 = N_00 * N_02 | 1155.0 | 27.5 1.0 42.0 |
Mike's age, decreased by the age of his N_00 -year-old sister, is N_01 . Mike's age, increased by his uncle's age, is N_02 . What age is mike's uncle? | v0 = N_00 + N_01 <BRG> v0 + v2 = N_02 | 38.0 15.0 | 4.0 11.0 53.0 |
Working alone, Ryan can dig a N_00 ft by N_00 ft hole in five hours. Castel can dig the same hole in six hours. How long would it take them if they worked together? | 1.0 / 5.0 * v0 + 1.0 / 6.0 * v0 = 1.0 | 2.72727272727 | 10.0 |
The sum of the ages of a brother and sister is N_00 . If four times the brother's age is subtracted from three times the sister's age, the difference is N_01 . | 3.0 * v0 - 4.0 * v1 = N_01 <BRG> v1 + v0 = N_00 | 17.0 10.0 | 27.0 11.0 |
The sum of a two-digit number is N_00 . The number with the digits interchanged is N_01 times the sum of the digits. Find the original number. | 10.0 * v0 + v1 - N_01 * v0 - N_01 * v1 = 0.0 <BRG> v0 + v1 = N_00 | 4.0 5.0 | 9.0 6.0 |
The difference between two numbers is N_00 . The sum of these numbers is N_01 . Find the numbers. | v0 + v1 = N_01 <BRG> v0 - v1 = N_00 | 13.0 49.0 | 36.0 62.0 |
Mike invested $ N_00 for one year. He invested part of it at N_01 and the rest at N_02 . At the end of the year, he earned $ N_03 in interest. How much did he invest at each rate? | N_02 * v0 + N_01 * v1 = N_03 <BRG> v1 + v0 = N_00 | 1800.0 4200.0 | 6000.0 0.09 0.11 624.0 |
One pan pizza and two cheeseburgers provide N_00 calories. Two pan pizzas and one cheeseburger provide N_01 calories. Find the caloric content of each item. | 1.0 * v0 + 2.0 * v1 = N_00 <BRG> 2.0 * v0 + 1.0 * v1 = N_01 | 1040.0 910.0 | 2860.0 2990.0 |
A number added to N_00 is equal to N_01 less than four times the number. What is the number? | v0 - 4.0 * v0 = - 1.0 * N_00 - N_01 | 12.0 | 6.0 30.0 |
Hollis is paying off two student loans. One loan charges N_02 interest per year. The other loan charges N_00 interest per year. He owes $ N_01 more on the N_02 loan than he does on the other. Last year he paid a total of $ N_03 interest. How much does he owe on each loan? | N_02 * v0 + N_00 * v1 = N_03 <BRG> v0 - v1 = N_01 | 4700.0 3200.0 | 0.09 1500.0 0.07 617.0 |
Two cars start from the same place and travel in opposite directions. One runs at an average rate which is N_00 kilometers per hour faster than the other. Find their rates if, after N_01 hours, they are N_02 km apart. | N_01 * v0 + N_01 * v0 = N_02 - N_01 * N_00 | 46.5 | 24.0 6.0 702.0 |
The sum of two numbers is N_00 . If the larger number is N_01 more than three times the smaller, find the larger number. | v0 - 3.0 * v1 = N_01 <BRG> v0 + v1 = N_00 | 5.0 -3.0 | 2.0 14.0 |
The sum of two numbers is N_00 . One number is N_01 more than twice the other. Find the smallest number. | v0 - 2.0 * v1 = N_01 <BRG> v0 + v1 = N_00 | 9.0 4.0 | 13.0 1.0 |
The sum of two numbers is N_00 . The difference between the same two numbers is N_01 . What are the two numbers? | v0 + v1 = N_00 <BRG> v0 - v1 = N_01 | 36.0 45.0 | 81.0 9.0 |
The sum of two numbers is N_00 . The second number is three times as much as the first number. What are the two numbers? | v0 + v1 = N_00 <BRG> v1 - 3.0 * v0 = 0.0 | 4.25 12.75 | 17.0 |
Two numbers have a sum of N_00 . Their difference is N_01 . What are the two numbers? | v0 + v1 = N_00 <BRG> v0 - v1 = N_01 | 21.0 26.0 | 47.0 5.0 |
The sum of two numbers is N_00 , and their difference is N_01 . Find the numbers. | v0 + v1 = N_00 <BRG> v0 - v1 = N_01 | 78.0 62.0 | 140.0 16.0 |
Eight years ago, Hold was N_00 times older than her son. Today, she is exactly N_01 times as old as her son. How old are both Mrs. Hold and her son today? | v0 - N_00 * v1 = - 1.0 * N_00 * 8.0 + 8.0 <BRG> v0 - N_01 * v1 = 0.0 | 36.0 12.0 | 7.0 3.0 |
If the price of copper is N_00 cents/lb and the price of zinc is N_01 cents/lb, how many pounds of copper and zinc should be mixed to make N_02 lb of brass selling for N_03 cents per pound? | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 30.0 40.0 | 65.0 30.0 70.0 45.0 |
Masc is N_00 years older than Sam, and the sum of their ages is N_01 . What are their ages? | v0 + v1 = N_01 <BRG> v0 - v1 = N_00 | 10.0 17.0 | 7.0 27.0 |
Two numbers differ by N_00 . The larger number is N_01 less than twice the smaller number. Find the numbers. | 2.0 * v0 - v1 = N_01 <BRG> v1 - v0 = N_00 | 26.0 16.0 | 10.0 6.0 |
N_00 exceeds six times a number by N_01 . What is the number? | 6.0 * v0 = N_00 - N_01 | 73.0 | 508.0 70.0 |
You can paint a certain room in N_00 hours. Your brother can do it in N_01 hours. How long does it take the two of you working together? | 1.0 / N_00 * v0 + 1.0 / N_01 * v0 = 1.0 | 1.71428571429 | 3.0 4.0 |
In a N_00 -digit number, the units digit is N_01 more than the tens digit. If the digits are reversed the new number is N_02 more than thrice the original number. find the original number | 10.0 * v0 + v1 - 3.0 * v0 - 3.0 * 10.0 * v1 = N_02 <BRG> v0 - v1 = N_01 | 5.0 1.0 | 2.0 4.0 6.0 |
Walt made an extra N_00 last year from a part-time job. He invested part of the money at N_01 and the rest at N_03 . He made a total of $ N_02 in interest. How much was invested at N_03 ? | N_01 * v0 + N_03* v1 = N_02 <BRG> v1 + v0 = N_00 | 4000.0 5000.0 | 9000.0 0.09 770.0 0.08 |
One number is N_00 more than N_01 times the other, and their sum is N_02 . What are the numbers? | v0 - N_01 * v1 = N_00 <BRG> v0 + v1 = N_02 | 19.0 8.0 | 3.0 2.0 27.0 |
Mr. Wise bought $ N_00 worth of stock, some at $ N_01 per share and some at $ N_02 per share. If he bought a total of N_03 shares of stock, how many of each did he buy? | N_01 * v0 + N_02 * v1 = N_00 <BRG> v0 + v1 = N_03 | 400.0 50.0 | 1950.0 3.0 4.5 450.0 |
Christopher is N_00 times as old as Gabriela. Nine years ago, Christopher was N_01 times as old as Gabriela. How old is Christopher now? | v0 - N_01 * v1 = - 1.0 * N_01 * 9.0 + 9.0 <BRG> v0 - N_00 * v1 = 0.0 | 24.0 12.0 | 2.0 5.0 |
A man rows a boat N_00 feet upstream against a constant current in N_01 minutes. He then rows N_02 feet downstream (with the same current) in N_03 minutes. Find the speed of the current and the equivalent rate at which he can row in still water. | N_03 * v0 + N_03 * v1 = N_02 <BRG> N_01 * v0 - N_01 * v1 = N_00 | 40.0 10.0 | 300.0 10.0 350.0 7.0 |
Olga has N_00 times as many dimes as nickels. If she has $ N_01 , how many of each coin does she have? | 0.05 * v0 + 0.1 * v1 = N_01 <BRG> N_00 * v0 - v1 = 0.0 | 6.0 30.0 | 5.0 3.3 |
A woman is three times as old as her son, and the sum of their ages is N_00 . Find each person's age. | v0 + v1 = N_00 <BRG> v1 - 3.0 * v0 = 0.0 | 13.0 39.0 | 52.0 |
You invested a total of $ N_00 in N_01 different banks. One bank pays N_02 interest, and the other bank pays N_03 interest. If you earn a total of $ N_04 in interest for the first year, how much did you invest in each bank? | N_02 * v0 + N_03* v1 = N_04 <BRG> v1 + v0 = N_00 | 1700.0 3300.0 | 5000.0 2.0 0.04 0.065 282.5 |
Mr. Herman had $ N_00 , and Mr. Chandra had $ N_01 . After each of them had paid for a concert ticket, Mr. Herman had six times as much money as Mr. Chandra. How much money did Mr. Chandra have left? | #NAME? | 71.0 | 125.0 80.0 |
Michael bought two used cars and fixed them up. He sold the first one for a N_00 profit and the second for a N_01 profit. He made a total profit of N_02 by selling these cars. The price that Michael paid for the first car was N_03 less than the price for the second car. What was the selling price of each car? | N_01 * v0 +N_00* v1 =N_02 <BRG> v0 - v1 = N_03 | 4500.0 7100.0 | 0.35 0.15 2640.0 2600.0 |
If the larger of two integers, whose sum is N_00 , is divided by the smaller, the quotient is N_01 , and the remainder is N_02 . What are the numbers? | v0 - N_01 * v1 = N_02 <BRG> v0 + v1 = N_00 | 75.0 13.0 | 88.0 5.0 10.0 |
Adult tickets for a play cost $ N_00 , and child tickets cost $ N_01 . If there were N_02 people at a performance and the theater collected $ N_03 from ticket sales, how many children attended the play? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 18.0 6.0 | 16.0 9.0 24.0 258.0 |
Hotels collect N_00 percent sale tax on all sales. If the total sales including tax are N_01 , find the portion that is the tax. | v0 + 0.01 * N_00 * v0 = N_01 | 1017.59615385 | 4.0 1058.3 |
Two cars traveling in opposite directions were N_00 km apart at the end of two hrs. If one car travels N_01 kph faster than the other, find the average speed of the slower car. | 2.0 * v0 + 2.0 * v1 = N_00 <BRG> v1 - v0 = N_01 | 87.0 93.0 | 360.0 6.0 |
How much N_00 anti-freeze should be mixed with N_01 anti-freeze to get N_02 liters of N_03 anti-freeze? | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 2.0 8.0 | 0.2 0.6 10.0 0.28 |
One number is N_00 more than twice the second number. Their total is N_01 . Find the numbers. | v0 - 2.0 * v1 = N_00 <BRG> v0 + v1 = N_01 | 18.0 7.0 | 4.0 25.0 |
Suppose you combine ingots of N_00 copper alloy and N_01 copper alloy to create N_02 kg of N_03 copper alloy. How many kilograms of each do you need? | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 32.0 8.0 | 0.25 0.5 40.0 0.45 |
The sum of a certain number and a second number is N_00 . The first number minus the second is N_01 . Find the numbers. | v0 + v1 = N_00<BRG> v0 - v1 = N_01 | -47.0 5.0 | -42.0 52.0 |
Jason is six times as old as Kate. In two years, Jason will be twice as old as Kate is then. How old is Jason now? | v0 - 2.0 * v1 = 2.0 * 2.0 - 2.0 <BRG> v0 - 6.0 * v1 = 0.0 | 0.5 3.0 | null |
Anne and Nancy use a metal alloy that is N_00 copper to make jewelry. How many ounces of an N_01 alloy must be mixed with a N_02 alloy to form N_03 ounces of the desired alloy? | N_01 * v0 + N_02 * v1 = N_03 * N_00 <BRG> v0 + v1 = N_03 | 45.0 63.0 | 0.1975 0.18 0.21 108.0 |
When you reverse the digits in a certain two-digit number, you decrease its value by N_00 . What is the number if the sum of its digits is N_01 ? | 10.0 * v0 + v1 - 10.0 * v1 - v0 = - 1.0 * N_00 <BRG> v1 + v0 = N_01 | 4.0 1.0 | 27.0 5.0 |
In history class, the girl to boy ratio is N_00 to N_01 . If there are a total of N_02 students, how many girls are there? | N_00 * v0 - N_01 * v1 = 0.0 <BRG> v0 + v1 = N_02 | 32.0 36.0 | 9.0 8.0 68.0 |
Ruffy is three-fourths as old as Orlie. Four years ago, Ruffy was N_00 year more than half old as Orlie. How old is each? | v0 - 0.5 * v1 = - N_00 * 0.5 * 4.0 + N_00 + 4.0 <BRG> v0 - 0.75 * v1 = 0.0 | 9.0 12.0 | 1.0 |
Keil is going to make N_00 pounds of mixed nuts for a party. Peanuts cost N_01 per pound, and fancy nuts cost N_02 per pound. If Keil can only spend N_03 on nuts, how many pounds of each should he buy? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 8.0 5.0 | 13.0 2.0 7.5 70.0 |
One whole number is three times a second. If N_00 is added to the smaller number, the result equals N_01 more than the larger number. Find both numbers. | v0 - v1 = N_01 - N_00 <BRG> 3.0 * v0 - v1 = 0.0 | 7.0 21.0 | 20.0 6.0 |
A coffee merchant has coffee beans that sell for $ N_00 per pound and $ N_01 per pound. The two types are to be mixed to create N_02 lb of a mixture that will sell for $ N_03 per pound. How much of each type of bean should be used in the mixture? | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 25.0 75.0 | 9.0 12.0 100.0 11.25 |
The sum of N_00 numbers is N_01 , and one number is N_02 less than the other. | v0 + v1 = N_01 <BRG> v0 - v1 = N_02 | 23.0 32.0 | 2.0 55.0 9.0 |
There were N_00 people at a play. Admission was $ N_01 for adults and $ N_02 for children. The receipts were $ N_03 . How many adults and how many children attended the play? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 203.0 226.0 | 429.0 1.0 0.75 372.5 |
How many grams of salt need to be added to N_00 grams of a N_01 salt solution in order to increase the salt content to N_02 ? | v0 = 0.01 * N_00 * N_02 - 0.01 * N_00 *N_01 | 3.0 | 60.0 0.2 0.25 |
Ten years ago, a man was as old as his wife is now. The man is now twice as old as his wife back then. How old are they both now? | 2.0 * v0 - v1 = 10.0 <BRG> v1 - v0 = 10.0 | 30.0 20.0 | null |
The sum of two numbers is N_00 . One number is ten more than twice the other number. | v0 - 2.0 * v1 = 10.0 <BRG> v0 + v1 = N_00 | 50.0 20.0 | 70.0 |
It cost a family of seven a total of $ N_00 for general admission tickets to the San Diego Zoo. If adult tickets cost $ N_01 and children's tickets cost $ N_02 , how many adult tickets were purchased? | N_01 * v0 + N_02 * v1 = N_00 <BRG> v0 + v1 = 7.0 | 4.0 3.0 | 119.0 21.0 14.0 |
How much water must be added to N_00 ml of a N_01 alcohol solution to obtain a N_02 alcohol solution? | N_02 * v0 = N_00 * N_00 - N_00 * N_02 | 50.0 | 75.0 0.75 0.45 |
Susan wants to mix N_00 pounds of Virginia peanuts that cost $ N_01 a pound with Spanish peanuts that cost $ N_02 a pound to obtain a mixture that costs $ N_03 a pound. How many pounds of Spanish peanuts should she use? | N_02 * v0 - N_03 * v0 = N_03 * N_00 - N_01 | -76.25 | 10.0 3.5 3.0 3.4 |
A solution of N_00 glycol is held in a N_01 -gallon tank. A N_02 solution of glycol is held in a N_03 -gallon tank. How much of the two tanks must be added together to have a N_04 -gallon tank of N_05 glycol? | N_00 * v0 + N_02 * v1 = N_04 * N_05 <BRG> v0 + v1 = N_04 | 118.918918919 81.0810810811 | 0.35 400.0 0.72 190.0 200.0 0.5 |
Three years ago, X's age was double of Y's. Seven years hence, the sum of their ages will be N_00 years. What is the age of X today? | v0 - 2.0 * v1 = - 1.0 * 2.0 * 3.0 + 3.0 <BRG> v0 + v1 = N_00 - 7.0 - 7.0 | 45.0 24.0 | 83.0 |
A specialty coffee store creates a special mix of two coffees at two different prices: $ N_02 and $ N_00 per pound each. How many pounds of the $ N_00 coffee should be mixed with N_01 pounds of $ N_02 coffee to sell the mixture for $ N_03 per pound? | N_00 * v0 - N_03 * v0 = N_03 * N_01 - N_01 * N_02 | 68.25 | 7.28 7.0 6.42 7.2 |
During the early N_00 s, kelly invested N_01 into two different types of accounts within a bank: certificates of deposit and savings account. For her accounts, she received N_02 interest for her certificates of deposit and N_03 for her savings account. In total, she earned N_04 for the year. How much money was invested... | N_02 * v0 + N_03* v1 = N_04 <BRG> v1 + v0 = N_01 | 3000.0 5000.0 | 1990.0 8000.0 0.08 0.06 580.0 |
A car radiator contains N_00 liters of a N_01 antifreeze solution. How many liters will have to be replaced with pure antifreeze if the resulting solution is to be N_02 antifreeze? | N_01 * v0 - v0 = N_01* N_00 - N_02 * N_00 | 2.85714285714 | 10.0 0.3 0.5 |
Two-thirds of a number increased by three-fourths is five-thirds. What is the number? | 0.67 * v0 = 1.67 - 0.75 | 1.375 | null |
Three times one number added to another is N_00 . Twice the first number minus the other number is N_01 . What are the numbers? | 3.0 * v0 + v1 = N_00 <BRG> 2.0 * v0 - v1 = N_01 | 3.0 5.0 | 14.0 1.0 |
How many quarts of pure antifreeze must be added to N_00 quarts of a N_01 antifreeze solution to obtain a N_02 antifreeze solution? | v0 - N_02 * v0 = N_02 * N_00 - N_01* N_00 | 0.5 | 4.0 0.1 0.2 |
A boat owner mixes together oil and gasoline to make N_00 gallons of fuel for N_01 $ per gallon. Oil costs $ N_02 per gallon, and gasoline costs $ N_03 per gallon. How many gallons of each should be used? | N_02 * v0 + N_03 * v1 = N_00 * N_01 <BRG> v0 + v1 = N_00 | 7.0 5.0 | 12.0 8.0 15.0 3.0 |
Gary drove to Sarnia. Part of the trip was along major highways, and the rest was along country roads. The speed limit is N_00 km/h on the highway and N_01 km/h on the other roads. He spent a total of N_02 hours driving N_03 km. Write a system of equations that would allow you to find how much time he spent on each typ... | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 4.5 7.5 | 100.0 80.0 12.0 1050.0 |
Every morning, Don Miguel exercises by walking a certain distance at an average of N_00 kph, rests for N_01 hours. And rides back along the same road on his chauffer-driven limousine at an average speed of N_02 kph. If the total time of travel is N_03 hours, how far does he walk? | 1.0 / N_00 * v0 + 1.0 / N_02 * v0 = N_03 - N_01 | 3.437625 | 4.0 0.3333 60.0 1.25 |
The sum of two numbers is N_00 . Adding four times the first number to the second number gives N_01 . Which one of the following equations expresses this problem algebraically? | 4.0 * v0 + v1 = N_01 <BRG> v0 + v1 = N_00 | 22.0 67.0 | 89.0 155.0 |
Mary is N_00 years older than Seth. In a year, she will be N_01 times as old as he is. How old are they? | v0 - N_01 * v1 = N_01 * 1.0 - 1.0 <BRG> v0 - v1 = N_00 | 3.5 12.5 | 9.0 3.0 |
If N_00 kilos of oranges and N_02 kilos of apples cost N_01 while N_02 kilos of oranges and N_03 kilos of apples cost N_04 , what is the cost of each per kilo? | N_00 * v0 + N_02 * v1 = N_01 <BRG> N_02 * v0 + N_03 * v1 = N_04 | 29.0 49.0 | 6.0 419.0 5.0 7.0 488.0 |
The difference between two numbers is N_00 . Three times the larger number is N_01 times the smaller. What are the numbers? | 3.0 * v0 - N_01 * v1 = 0.0 <BRG> v0 - v1 = N_00 | 24.0 8.0 | 16.0 9.0 |
Three times a number, increased by four, is one half the same number, decreased by one. What is the number? | 3.0 * v0 - 0.5 * v0 = - 1.0 * 1.0 - 4.0 | -2.0 | null |
You invest $ N_00 in two accounts, paying N_01 and N_02 annual interest, respectively. At the end of the year, the accounts earn the same interest. How much was invested at each investment? | N_01 * v0 - N_02 * v1 = 0.0 <BRG> v0 + v1 = N_00 | 4000.0 3200.0 | 7200.0 0.08 0.1 |
Two times a number plus three times another number equals N_00 . The sum of the two numbers is N_01 . What are the two numbers? | 2.0 * v0 + 3.0 * v1 = N_00 <BRG> v0 + v1 = N_01 | -1.0 8.0 | 13.0 7.0 |
Bus A is N_00 miles due east of Bus B. Both busses start driving due west at constant speeds at the same time. It takes Bus A N_01 hours to overtake Bus B. If they had started out at the same time, had driven at the same constant speeds, but had driven toward one another, they would have met in N_02 hours. What is the ... | N_02 * v0 + N_02 * v1 = N_00 <BRG> N_01 * v0 - N_01 * v1 = N_00 | 45.0 30.0 | 150.0 10.0 2.0 |
Justin can mow a lawn in N_00 hours. David can mow a lawn in N_01 hours. How long will it take them to mow one lawn together? | 1.0 / N_00 * v0 + 1.0 / N_01 * v0 = 1.0 | 1.2 | 2.0 3.0 |
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make N_00 pounds of feed worth $ N_01 per pound by mixing one kind worth $ N_02 per pound with another worth $ N_03 per pound. How many pounds of the cheaper kind should they use in the mix? | N_02 * v0 + N_03 * v1 = N_00 * N_01 <BRG> v0 + v1 = N_00 | 14.2105263158 12.7894736842 | 27.0 0.26 0.17 0.36 |
For a party, adult tickets were sold at $ N_00 , and child tickets were sold at $ N_01 . there were N_02 tickets sold for a total value of $ N_03 . How many of each type of ticket were sold? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 100.0 40.0 | 15.0 10.0 140.0 1600.0 |
You have a N_00 solution and a N_01 solution. How many liters of each solution do you need to mix when you need N_02 liters of a N_03 alcohol solution. | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 80.0 120.0 | 0.2 0.7 200.0 0.5 |
A cruise boat travels N_00 miles downstream in N_01 hours and returns to its starting point upstream in N_02 hours. Find the speed of the stream. | N_01 * v0 + N_01 * v1 = N_00 <BRG> N_02 * v0 - N_02 * v1 = N_00 | 12.5 7.5 | 60.0 3.0 12.0 |
Tap A is able to fill a bath in N_00 minutes, and tap B is able to fill the same bath in N_01 minutes. How long would it take them to fill the same bath if they are turned on together? | 1.0 / N_00 * v0 + 1.0 / N_01 * v0 = 1.0 | 12.0 | 20.0 30.0 |
You are N_00 times as old as your sister. In N_01 years time, you will be twice as old as your sister. What are your ages now? | v0 - 2.0 * v1 = 2.0 * N_01 - N_01 <BRG> v0 - N_00 * v1 = 0.0 | 4.0 16.0 | 4.0 8.0 |
There are N_00 Douglas fir and ponderosa pine trees in a section of forest bought by Sawz Logging Co. The company paid an average of $ N_01 for each Douglas fir and $ N_02 for each ponderosa pine. If the company paid $ N_03 for the trees, how many of each kind did the company buy? | N_01 * v0 + N_02 * v1 =N_03 <BRG> v0 + v1 = N_00 | 350.0 500.0 | 850.0 300.0 225.0 217500.0 |
A number is N_00 times the sum of its digits. The tens digit is N_01 greater than the units digit. Find the number. | 10.0 * v0 + v1 - N_00 * v0 - N_00 * v1 = 0.0 <BRG> v0 - v1 = N_01 | 7.0 2.0 | 8.0 5.0 |
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