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.