Patty can buy 5 packs of cookies because 15 / 3 = 5. Patty gets 120 cookies because 5 x 24 = 120. Patty would need to pay 12 cookies per week because 3 x 4 = 12. Patty can avoid 10 weeks of chores because 120 / 12 = 10.
The answer: 10
Reverse engineering the question: Patty decides that to convince her brother and sister to do her chores in exchange for cookies. Patty agrees to give them 3 cookies for every chore they do. Each kid normally has 4 chores to do per week. Patty has $15 to buy cookies. Each pack of cookies contains 24 cookies and costs $3. How many weeks can Patty go without doing chores by paying her siblings with cookies?

Sarah has 12 / 6 = 2 pencils. Tim has 8 * 2 = 16 pencils.
The answer: 16
Reverse engineering the question: Tyrah has six times as many pencils as Sarah has. Tim has eight times as many pencils as Sarah. If Tyrah has 12 pencils, how many does Tim have?

First find Karen's net speed by subtracting the speed of the current: 10 mph - 4 mph = 6 mph. Then divide the length of the river by Karen's speed to find how long it takes her to paddle up it: 12 miles / 6 mph = 2 hours.
The answer: 2
Reverse engineering the question: Karen is paddling her canoe up a river against the current. On a still pond, Karen can paddle 10 miles per hour. The river flows in the opposite direction at 4 miles per hour. If the river is 12 miles long, how many hours will it take Karen to paddle up it?

The rectangular tables seat 7 * 10 = 70 pupils. The square tables will seat 90 - 70 = 20 pupils. The library needs 20 / 4 = 5 square tables.
The answer: 5
Reverse engineering the question:
A library has 7 rectangular tables and the remaining tables will be square tables. A rectangular table seats 10 pupils while a square table seats 4 pupils. How many square tables are needed so that 90 pupils can read at the same time?