Raeann, Wendy and Emma had a total of 68 buttons. The ratio of Wendy's buttons to Emma's buttons was at first 10 : 3. After Raeann and Wendy each gave half of their buttons away, the 3 children had 37 buttons left. How many buttons did Raeann and Wendy have at first?
| |
Raeann |
Wendy |
Emma |
Total |
| Before |
2 p |
10 u |
3 u |
68 |
| Change |
- 1 p |
- 5 u |
|
- 31 |
| After |
1 p |
5 u |
3 u |
37 |
Number of buttons that Raeann and Wendy gave away
= 68 - 37
= 31
1 p + 5 u = 31
1 p = 31 - 5 u --- (1)
1 p + 5 u + 3 u = 37
1 p + 8 u = 37
1 p = 37 - 8 u --- (2)
(1) = (2)
31 - 5 u = 37 - 8 u
8 u - 5 u = 37 - 31
3 u = 6
1 u = 6 ÷ 3 = 2
From (1)
1 p = 31 - 5 u
1 p = 31 - 5 x 2
1 p = 31 - 10 = 21
Number of buttons that Raeann and Wendy had at first
= 2 p + 10 u
= 2 x 21 + 10 x 2
= 42 + 6
= 48
Answer(s): 48
