Sam saved 4/7 of his paycheck and spent 2/5 of the remaining money. He was then left with $9. What was the original value of Sam's paycheck?
5/2
the amount left was
(1 - 4/7)(1 - 2/5) = 3/7 * 3/5 = 9/35 of the original amount.
So, 9/35 x = 9
x = 35
To find the original value of Sam's paycheck, we'll need to work backward from the information given.
Let's assume the original value of Sam's paycheck is represented by "x."
Sam saved 4/7 of his paycheck, which means he had (1 - 4/7) = 3/7 of his paycheck remaining.
Next, he spent 2/5 of the remaining money. This means he has (1 - 2/5) = 3/5 of the remaining money left.
According to the information, Sam has $9 left, which represents 3/5 of the remaining money.
To find the value of 1/5 of the remaining money, we can divide $9 by 3 and multiply by 5: (9/3) * 5 = $15.
Thus, 1/5 of the remaining money is $15, which means the original value of Sam's paycheck (x) can be found by multiplying it by 7/3: x = 15 * (7/3) = $35.
Therefore, the original value of Sam's paycheck was $35.