josh receives a weekly paycheck from his job. at the end of the week he has $52 remaining. throughout the week he spent a third of his paycheck at the mall and $8 for a new calculator. what the amount of his paycheck?
164
To find the amount of Josh's paycheck, we need to calculate the total amount he spent during the week.
First, we know that he spent 1/3 of his paycheck at the mall and $8 for a calculator. Let's represent the amount of his paycheck as "x".
The amount he spent at the mall can be calculated as (1/3)x, and the amount spent on the calculator is $8. So, the total amount he spent is (1/3)x + $8.
We also know that he has $52 remaining after all his expenses. So, we can set up the equation:
x - ((1/3)x + $8) = $52
To solve the equation, let's simplify it by removing the parentheses:
x - (1/3)x - $8 = $52
To solve for x, let's combine like terms by subtracting (1/3)x:
(2/3)x - $8 = $52
Next, let's isolate the variable x by adding $8 to both sides:
(2/3)x = $60
To eliminate the fraction coefficient, we can multiply both sides by its reciprocal, which is 3/2:
(3/2)(2/3)x = (3/2)($60)
The fraction coefficients cancel out, leaving us with:
x = ($90)
Therefore, Josh's paycheck is $90.