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.
The way you solved this problem was wrong.Aaron did not start out with 3/7 you have to work bacwards in the problem and that is what is confusing me
He spent 3/7 which left him with 4/7 !!!
7/7 - 3/7 = 4/7
then he gave away 1/4 of his 4/7
1 - 1/4 = 3/4
so he is left with
4/7 * 3/4
Look at this simpler problem:
http://www.jiskha.com/display.cgi?id=1423783632
What did he start with not left with plus he left with 120 dollars and he started with 3?I don't think that is resonable.
It's not suppoesd to be a fraction!!
he started with x
he spent 3/7 of x
then he had 4/7 of x left
he then gave his sister 1/4 of 4/7 of x
so he was left with 3/4 of 4/7 of x
that is 120
so
3/4 * 4/7 * x = 120
3/7 * x = 120
x = 40*7 = 280
===========================
NOW spend 3/7 * 280 = 120
280 - 120 = 160 left
now give your sister 1/4 of the 160 or 40
left with 160 - 40 = 120
sure enough
Believe it yet ?
HE HAD 280 dollars. That is the answer. It is not a fraction.
I apologize for any confusion. Let's work backward to find the amount of money Aaron had in the beginning.
Given:
- Aaron had $120 left after giving 1/4 of the remainder to his sister.
- Before giving money to his sister, Aaron spent 3/7 of his money.
To find the amount Aaron had at the beginning, we'll follow these steps:
1. Find the amount of money Aaron had after giving 1/4 of the remainder to his sister:
Since Aaron has $120 left, we can assume that this amount is 3/4 of the remainder (after spending 3/7). We can set up the equation: 3/4 * remainder = $120.
2. Determine the remainder after spending 3/7:
To find the remainder, we assume it is 4/7 of the initial amount. So, the equation becomes: 4/7 * initial amount = remainder.
3. Substitute the value of the remainder into the equation:
Using the value of the remainder obtained in step 2, we substitute it into the equation from step 1: 3/4 * (4/7 * initial amount) = $120.
4. Solve for the initial amount:
By solving the equation from step 3, you can find the initial amount that Aaron started with.
I hope this explanation helps you understand the process better.