Ahmad, Luke and Ethan had a total of 107 beads. The ratio of the number of beads that Luke had to the number of beads that Ethan had was 4 : 5. After Ahmad and Luke each gave away half of their beads, the 3 children had 81 beads left. How many beads did Luke and Ethan have at first?
| |
Ahmad |
Luke |
Ethan |
Total |
| Before |
2 p |
4 u |
5 u |
107 |
| Change |
- 1 p |
- 2 u |
|
- 26 |
| After |
1 p |
2 u |
5 u |
81 |
Total number of beads that Ahmad and Luke gave away
= 107 - 81
= 26
1 p + 2 u = 26 --- (1)
1 p + 2 u + 5 u = 81
1 p + 7 u = 81 --- (2)
(2) - (1)
(1 p + 7 u) - (1 p + 2 u) = 81 - 26
7 u - 2 u = 55
5 u = 55
1 u = 55 ÷ 5 = 11
Total number of beads that Luke and Ethan had at first
= 4 u + 5 u
= 9 u
= 9 x 11
= 99
Answer(s): 99
