Ryan, Zane and Brandon had a total of 220 beads. The ratio of the number of beads that Zane had to the number of beads that Brandon had was 8 : 9. After Ryan and Zane each gave away half of their beads, the 3 children had 164 beads left. How many beads did Zane and Brandon have in the end?
| |
Ryan |
Zane |
Brandon |
Total |
| Before |
2 p |
8 u |
9 u |
220 |
| Change |
- 1 p |
- 4 u |
|
- 56 |
| After |
1 p |
4 u |
9 u |
164 |
Total number of beads that Ryan and Zane gave away
= 220 - 164
= 56
1 p + 4 u = 56 --- (1)
1 p + 4 u + 9 u = 164
1 p + 13 u = 164 --- (2)
(2) - (1)
(1 p + 13 u) - (1 p + 4 u) = 164 - 56
13 u - 4 u = 108
9 u = 108
1 u = 108 ÷ 9 = 12
Total number of beads that Zane and Brandon had in the end
= 4 u + 9 u
= 13 u
= 13 x 12
= 156
Answer(s): 156
