Let b be the number of trips Bill makes and j be the number Jean makes. We know that b + j = 40, and j = b + 6. Substituting the first equation into the second equation, we get b + b + 6 = 40. Combining like terms, we get 2b + 6 = 40. Subtracting 6 from both sides, we get 2b = 34. Dividing both sides by 2, we get b = 17. Substituting that value back into j = b + 6, we get j = 17 + 6 = 23.
The answer: 23
Reverse engineering the question: Bill and Jean are both cleaning out their garages. Bill makes a certain number of trips to the dump and Jean makes that many trips plus 6. If they make 40 trips total, how many trips does Jean make?
Reasoning and answer: They made $10 because 2 x 5 = 10. They made $1 off single pieces because 100 x .01 = 1. They made $.9 off double pieces because 45 x .02 = .9. They made $1.5 off triple pieces because 50 x .03 = 1.5. They earned $3.4 off the first three types because 1 + .9 + 1.5 = 3.4. They earned $6.6 off the quadruple pieces because 10 - 3.4 = 6.6. They sold 165 quadruple pieces because 6.6 / .04 = 165.
The answer: 165
What was the question?
Question: Michael and Thomas are selling their lego collections. They agree to split any money they earn. They sell them based on how many circles are on top. Each circle costs 1 cent. They earned $5 each after selling 100 single pieces, 45 double pieces, 50 triple pieces and a number of quadruple pieces. How many quadruple pieces did they sell?
She has 24 / 2 = 12 dresses with pockets. Of those 12 / 3 = 4 have 2 pockets. So 12 - 4 = 8 have three pockets. So the dresses with 2 pockets have 2 * 4 = 8 pockets. The other dresses contribute 8 * 3 = 24 pockets. So she has a total of 8 + 24 = 32 pockets.
The answer: 32
Reverse engineering the question: Janet has 24 dresses. Half of them have pockets. Of those, a third have 2 pockets and the rest have 3 pockets. How many total pockets do her dresses have?
Reasoning and answer: Cindi bought 30 / 0.50 = 60 pencils. Marcia bought 2 * 60 = 120 pencils. Donna bought 3 * 120 = 360 pencils. Altogether, Donna and Marcia bought 120 + 360 = 480 pencils.
The answer: 480
What was the question?
Question: Donna bought 3 times as many pencils as Marcia did. Marcia bought double the number of pencils as Cindi did. How many pencils did Donna and Marcia buy altogether if Cindi spent $30 on $0.50 pencils?
If you add all the songs together, Gabe's playlist is 3 + 2 + 3 = 8 minutes long. During the 40 - minute car ride, Gabe can listen to his 8 - minute playlist 40 / 8 = 5 times.
The answer: 5
Reverse engineering the question: Gabe has three songs on his playlist. "The Best Day" is 3 minutes, "Raise the Roof" is 2 minutes, and "Rap Battle" is 3 minutes. How many times can Gabe listen to his entire playlist on the 40-minute ride to his wrestling match?
Let the number of cans of corn she bought be a. Twice the number of corn cans is 2 * a = 2a. The 35 cans of peas were 15 more than twice the number of corn cans which means 15 + 2a = 35. Solving the equation: 2a = 20. a = 20 / 2 = 10 cans of corn.
The answer: 10
Reverse engineering the question:
Beth went shopping. She bought 15 more cans of peas than twice the number of cans of corn that she bought. If she bought 35 cans of peas, how many cans of corn did she buy?