Final answer:
Ethan needs to make at least $812.50 in his paycheck to cover the remaining amount needed for the dirt bike.
Step-by-step explanation:
To find out how much money Ethan must make in his paycheck, we need to subtract the amount he has already saved from the total amount he needs. So, $500 - $175 = $325. Two-fifths of his paycheck will cover this remaining amount, so we need to find the value of two-fifths of his paycheck that equals $325.
To do this, we can set up an equation. Let's say his paycheck is equal to x. Then, two-fifths of x is equal to $325, or (2/5)x = $325.
To solve for x, we can multiply both sides of the equation by 5/2: (5/2)(2/5)x = (5/2)$325. The 2/5's cancel out, and we are left with x = (5/2)$325.
Simplifying further, we get x = $812.50. Therefore, Ethan must make at least $812.50 in his paycheck to cover the remaining amount needed for the dirt bike.