Dana, Vanessa and Victoria had a total of 89 coins. The ratio of Vanessa's coins to Victoria's coins was at first 12 : 5. After Dana and Vanessa each gave half of their coins away, the 3 children had 52 coins left. How many coins did Dana and Victoria have at first?
| |
Dana |
Vanessa |
Victoria |
Total |
| Before |
2 p |
12 u |
5 u |
89 |
| Change |
- 1 p |
- 6 u |
|
- 37 |
| After |
1 p |
6 u |
5 u |
52 |
Number of coins that Dana and Vanessa gave away
= 89 - 52
= 37
1 p + 6 u = 37
1 p = 37 - 6 u --- (1)
1 p + 6 u + 5 u = 52
1 p + 11 u = 52
1 p = 52 - 11 u --- (2)
(1) = (2)
37 - 6 u = 52 - 11 u
11 u - 6 u = 52 - 37
5 u = 15
1 u = 15 ÷ 5 = 3
From (1)
1 p = 37 - 6 u
1 p = 37 - 6 x 3
1 p = 37 - 18 = 19
Number of coins that Dana and Victoria had at first
= 2 p + 5 u
= 2 x 19 + 5 x 3
= 38 + 15
= 53
Answer(s): 53
