John, Brandon and Dylan had a total of 110 buttons. The ratio of the number of buttons that Brandon had to the number of buttons that Dylan had was 4 : 9. After John and Brandon each gave away half of their buttons, the 3 children had 91 buttons left. How many buttons did Brandon and Dylan have in the end?
| |
John |
Brandon |
Dylan |
Total |
| Before |
2 p |
4 u |
9 u |
110 |
| Change |
- 1 p |
- 2 u |
|
- 19 |
| After |
1 p |
2 u |
9 u |
91 |
Total number of buttons that John and Brandon gave away
= 110 - 91
= 19
1 p + 2 u = 19 --- (1)
1 p + 2 u + 9 u = 91
1 p + 11 u = 91 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 2 u) = 91 - 19
11 u - 2 u = 72
9 u = 72
1 u = 72 ÷ 9 = 8
Total number of buttons that Brandon and Dylan had in the end
= 2 u + 9 u
= 11 u
= 11 x 8
= 88
Answer(s): 88
