Troy saved 2/3 of his paycheck and spent 1/3 of the remaining money. He was then left with $12. What was the original value of Troy's paycheck?

2/3 * 2/3 * p = 12

4/9 * p = 12
p = 9 * 3 = 27

2/3 * 1/3 = 2/9

so
2/9 x = 12
solve for x

I assumed that "remaining money" is what he saved.

Oobleck assumed that "remaining money" was what he did not save.
Who knows ?

To determine the original value of Troy's paycheck, we can work backwards from the information given.

Let's call the original value of Troy's paycheck "P".

Troy saved 2/3 of his paycheck, which means he had (1 - 2/3) = 1/3 of his paycheck remaining after saving.

He then spent 1/3 of the remaining money, which means he had (1 - 1/3) = 2/3 of the remaining money left.

We know that the remaining money is equal to $12, so we can set up the equation:

2/3 * P = $12

To solve for P, we can multiply both sides of the equation by 3/2:

2/3 * P * 3/2 = $12 * 3/2

Simplifying the equation:

P = $18

Therefore, the original value of Troy's paycheck was $18.