Andy had 20% fewer marbles than Henry. When Andy gave 80 marbles to Henry, the numbers of marbles he had left was half of what Henry had. How many marbles did Andy have in the begining?
Please help me
To solve this problem, let's break it down step by step:
1. Let's assume that the number of marbles Henry had initially was 'x'.
2. According to the problem, Andy had 20% fewer marbles than Henry. So, Andy had (0.2 * x) fewer marbles than Henry, which is 0.8x.
3. After giving 80 marbles to Henry, Andy was left with half the number of marbles that Henry had. That means Andy had (0.5 * x) marbles left, and Henry had (x + 80) marbles.
4. Now, we can set up an equation: (0.8x) = (0.5 * (x + 80)).
- The left side of the equation represents the number of marbles Andy had initially.
- The right side of the equation represents the number of marbles Andy had left after giving some marbles to Henry.
5. Let's solve this equation step by step:
0.8x = 0.5(x + 80) ⟹
0.8x = 0.5x + 40 ⟹
0.8x - 0.5x = 40 ⟹
0.3x = 40 ⟹
x = 40 / 0.3 ⟹
x ≈ 133.33
Therefore, Andy initially had approximately 133 marbles.