How much did Aaron start with?

Aaron spent 3/7 of his money. He gave 1/4 of the remainder to his sister. He had $120 left. How much money did he have in the beginning? Explain how you got your answer.

(3/7)x + (1/4 * 4/7x) + 120 = x

(3/7)x + (1/7)x + 120 = x

4/7x + 120 = x

120 = (3/7)x

120 / (3/7) = x

120 * (7/3) = x

840/3 = x

280 = x

Assume Aaron had x dollars

he gave 3/7 x away, so he has 4x/7 left.
he gives 1/4 of what he has left to his sister, so he has (3/4)(4x/7) left
(3/4)(4x/7) = 120
12x/28 = 120
x = 120(28/12) = $ 280

280

To find out how much Aaron started with, we need to work backwards from the given information. Let's go step by step:

1. Aaron spent 3/7 of his money. So, he has 1 - 3/7 = 4/7 of his money remaining.

2. Aaron gave 1/4 of the remainder to his sister. This means he has 1 - 1/4 = 3/4 of the remainder left.

3. The remaining money is $120.

To find out the initial amount, we need to reverse the process:

Step 2: 3/4 of the remainder is equal to $120, so we can set up the equation:

(3/4) * remainder = $120

Step 3: To isolate the remainder, we can multiply both sides of the equation by the reciprocal of (3/4), which is (4/3):

remainder = ($120) * (4/3)

Simplifying, we have:

remainder = $160

Step 4: Now, we know that 4/7 of the initial amount is equal to the remainder, which is $160. Let's set up the equation:

(4/7) * initial amount = $160

To isolate the initial amount, we can multiply both sides of the equation by the reciprocal of (4/7), which is (7/4):

initial amount = ($160) * (7/4)

Simplifying, we have:

initial amount = $280

Therefore, Aaron started with $280.