Tim, Fabian and Ethan had a total of 120 beads. The ratio of the number of beads that Fabian had to the number of beads that Ethan had was 4 : 5. After Tim and Fabian each gave away half of their beads, the 3 children had 90 beads left. How many beads did Fabian and Ethan have in the end?
| |
Tim |
Fabian |
Ethan |
Total |
| Before |
2 p |
4 u |
5 u |
120 |
| Change |
- 1 p |
- 2 u |
|
- 30 |
| After |
1 p |
2 u |
5 u |
90 |
Total number of beads that Tim and Fabian gave away
= 120 - 90
= 30
1 p + 2 u = 30 --- (1)
1 p + 2 u + 5 u = 90
1 p + 7 u = 90 --- (2)
(2) - (1)
(1 p + 7 u) - (1 p + 2 u) = 90 - 30
7 u - 2 u = 60
5 u = 60
1 u = 60 ÷ 5 = 12
Total number of beads that Fabian and Ethan had in the end
= 2 u + 5 u
= 7 u
= 7 x 12
= 84
Answer(s): 84
