Ahmad, Harry and Reggie had a total of 99 beads. The ratio of the number of beads that Harry had to the number of beads that Reggie had was 8 : 9. After Ahmad and Harry each gave away half of their beads, the 3 children had 72 beads left. How many beads did Harry and Reggie have at first?
| |
Ahmad |
Harry |
Reggie |
Total |
| Before |
2 p |
8 u |
9 u |
99 |
| Change |
- 1 p |
- 4 u |
|
- 27 |
| After |
1 p |
4 u |
9 u |
72 |
Total number of beads that Ahmad and Harry gave away
= 99 - 72
= 27
1 p + 4 u = 27 --- (1)
1 p + 4 u + 9 u = 72
1 p + 13 u = 72 --- (2)
(2) - (1)
(1 p + 13 u) - (1 p + 4 u) = 72 - 27
13 u - 4 u = 45
9 u = 45
1 u = 45 ÷ 9 = 5
Total number of beads that Harry and Reggie had at first
= 8 u + 9 u
= 17 u
= 17 x 5
= 85
Answer(s): 85
