Mark, Simon and Jack had a total of 37 buttons. The ratio of the number of buttons that Simon had to the number of buttons that Jack had was 2 : 7. After Mark and Simon each gave away half of their buttons, the 3 children had 29 buttons left. How many buttons did Simon and Jack have in the end?
| |
Mark |
Simon |
Jack |
Total |
| Before |
2 p |
2 u |
7 u |
37 |
| Change |
- 1 p |
- 1 u |
|
- 8 |
| After |
1 p |
1 u |
7 u |
29 |
Total number of buttons that Mark and Simon gave away
= 37 - 29
= 8
1 p + 1 u = 8 --- (1)
1 p + 1 u + 7 u = 29
1 p + 8 u = 29 --- (2)
(2) - (1)
(1 p + 8 u) - (1 p + 1 u) = 29 - 8
8 u - 1 u = 21
7 u = 21
1 u = 21 ÷ 7 = 3
Total number of buttons that Simon and Jack had in the end
= 1 u + 7 u
= 8 u
= 8 x 3
= 24
Answer(s): 24
