Zane, Harry and Perry had a total of 71 marbles. The ratio of the number of marbles that Harry had to the number of marbles that Perry had was 4 : 5. After Zane and Harry each gave away half of their marbles, the 3 children had 53 marbles left. How many marbles did Harry and Perry have at first?
| |
Zane |
Harry |
Perry |
Total |
| Before |
2 p |
4 u |
5 u |
71 |
| Change |
- 1 p |
- 2 u |
|
- 18 |
| After |
1 p |
2 u |
5 u |
53 |
Total number of marbles that Zane and Harry gave away
= 71 - 53
= 18
1 p + 2 u = 18 --- (1)
1 p + 2 u + 5 u = 53
1 p + 7 u = 53 --- (2)
(2) - (1)
(1 p + 7 u) - (1 p + 2 u) = 53 - 18
7 u - 2 u = 35
5 u = 35
1 u = 35 ÷ 5 = 7
Total number of marbles that Harry and Perry had at first
= 4 u + 5 u
= 9 u
= 9 x 7
= 63
Answer(s): 63
