Jason spent 1/4 of his money and an additional $10 on some books. He then spent 2/5 of the remaining money and an additional $8 on some DVD’s. If he was left with $130, how much money did he have at first?
If he started with $x, then
1/4 x on something, leaving 3/4 x
10 on books, leaving 3/4 x - 10
2/5 (3/4 x - 10) on something, leaving 3/5 (3/4 x - 10) = 9/20 x - 6
8 on DVD's, leaving 9/20 x - 14
so now you have
9/20 x - 14 = 130
9/20 x = 144
x = 144 * 20/9 = 320
To be sure, work out the actual amounts spent ...
Let's break down the problem step by step to find the solution.
Step 1: Find the amount of money Jason had left after buying books.
Jason spent 1/4 of his money, so he had 3/4 of his money remaining.
He also spent an additional $10 on books, so the amount of money remaining can be represented as (3/4)x - 10.
Step 2: Find the amount of money Jason had left after buying DVD's.
Jason spent 2/5 of the remaining money, which was (3/4)x - 10. So, the amount of money remaining is (3/5)[(3/4)x - 10].
He also spent an additional $8 on DVD's, so the new amount of money remaining can be represented as (3/5)[(3/4)x - 10] - 8.
Step 3: Set up an equation and solve for the initial amount of money Jason had.
The new amount of money remaining after buying DVD's is given as $130. So, we can set up the equation:
(3/5)[(3/4)x - 10] - 8 = 130.
Let's solve this equation: