How much did Aaron start with?
Aaron spent 3/7 of his money. He gave ¼ 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.
(4/7)(3/4) x = 120
To find out how much money Aaron had in the beginning, we can work backward. Let's go step by step using the information given.
1. Aaron spent 3/7 of his money: This means he kept 4/7 of his money.
2. He gave 1/4 of the remainder to his sister: This means he kept 3/4 of the remainder for himself.
3. He had $120 left: This is the amount he kept for himself (3/4 of the remainder).
To find the total amount of money Aaron had in the beginning, we need to find the amount of money he had after each step. Let's calculate it:
Step 1: Aaron kept 4/7 of his money, so the remaining fraction is 4/7.
Step 2: Aaron kept 3/4 of the remainder from step 1, so the remaining fraction is 3/4.
Step 3: Aaron had $120 left, which is equal to 3/4 of the remainder from step 2.
To solve for the remaining fraction, which represents the amount Aaron had in the beginning, we can set up an equation:
(3/4) * (3/4) * (4/7) * X = $120
Simplifying the equation:
9/16 * 4/7 * X = 120
36/112 * X = 120
X = (120 * 112) / 36
X = 373.33...
So, Aaron had approximately $373.33 in the beginning.