Mr.Wood went to the stores to buy school supplies for his children. He spent half of his money plus $5 at Store A. He then spent half of the remaining money plus $10 at Store B. At the end he had $25 left. How much money did Mr. Wood start with?
If he started with x, then after A he had
x/2 - 5 left. After B he had
(x/2-5)/2-10 left
So,
x - (x/2+5) - (x/2-5)/2-10 = 25
x = 150
after A = had 70
after B he had 25
To determine how much money Mr. Wood started with, we can work backward from the amount he had left at the end of his shopping trip.
Let's denote the initial amount of money Mr. Wood had as "X" dollars.
First, Mr. Wood spent half of his money plus $5 at Store A. This can be expressed as (X/2) + $5.
Next, he spent half of the remaining money plus $10 at Store B. Therefore, the amount he spent at Store B was [(X/2) - ((X/2) + $5)] + $10.
This expression simplifies to -($5) + $10, which yields -$5.
Now, we can set up an equation: X - [(X/2) + $5] - [(X/2) - ((X/2) + $5)] + $10 = $25.
Simplifying further, the equation becomes:
X - (X/2) - $5 - (X/2) + (X/2) + $5 + $10 = $25.
Combining like terms, we get:
X - X/2 - X/2 + X/2 - $5 + $5 + $10 = $25.
Simplifying even more:
X - X/2 - X/2 + X/2 = $25.
After canceling out like terms, we have:
X/2 = $25.
To solve for X, we can multiply both sides of the equation by 2:
X = $25 * 2.
Therefore, Mr. Wood started with $50.