Question

A number is multiplied by 7. Then 29 is added to the product. This sum is then divided by 2. The answer is 46. What was the original number?

Student's solution - The answer was 46. If this was the result of dividing by 2, the number at this point was 92. If this was the result of adding 29, the number at this point was 63. If this was the result of multiplying by 7, the original number was 9.

Solve this problem using a similar strategy.

A number is multiplied by 10. Then 32 is added to the product. This sum is then divided by 4. The answer is 28.

What was the original number?

Answer 1

For the student's solution, the student started with the final answer and then worked backwards.
Start your solution with
The answer was 28.

Working backwards, the sentence in the question after the answer is "This sum is then divided by 4."
Use the same thing as the student's solution, but switch out the different numbers.
If this was the result of dividing by 4, the number at this point was 112. (
`28*4=112`)
The next sentence in the question then says "Then 32 is added to the product."
Going off of the student's solution,
If this was the result of adding 32, the number at this point was 80. (
`112-32=80`)
Again looking at the question, "A number is multiplied by 10."
Going off of the student's solution,
If this was the result of multiplying by 10, the original number was 8. (
`(80)/(10)`)

The answer is 8.