Nicole, Linda and Gwen had a total of 164 coins. The ratio of Linda's coins to Gwen's coins was at first 4 : 7. After Nicole and Linda each gave half of their coins away, the 3 children had 124 coins left. How many coins did Nicole and Gwen have at first?
| |
Nicole |
Linda |
Gwen |
Total |
| Before |
2 p |
4 u |
7 u |
164 |
| Change |
- 1 p |
- 2 u |
|
- 40 |
| After |
1 p |
2 u |
7 u |
124 |
Number of coins that Nicole and Linda gave away
= 164 - 124
= 40
1 p + 2 u = 40
1 p = 40 - 2 u --- (1)
1 p + 2 u + 7 u = 124
1 p + 9 u = 124
1 p = 124 - 9 u --- (2)
(1) = (2)
40 - 2 u = 124 - 9 u
9 u - 2 u = 124 - 40
7 u = 84
1 u = 84 ÷ 7 = 12
From (1)
1 p = 40 - 2 u
1 p = 40 - 2 x 12
1 p = 40 - 24 = 16
Number of coins that Nicole and Gwen had at first
= 2 p + 7 u
= 2 x 16 + 7 x 12
= 32 + 84
= 116
Answer(s): 116
