Jane, Fiona and Natalie had a total of 193 coins. The ratio of Fiona's coins to Natalie's coins was at first 8 : 9. After Jane and Fiona each gave half of their coins away, the 3 children had 137 coins left. How many coins did Jane and Fiona have at first?
| |
Jane |
Fiona |
Natalie |
Total |
| Before |
2 p |
8 u |
9 u |
193 |
| Change |
- 1 p |
- 4 u |
|
- 56 |
| After |
1 p |
4 u |
9 u |
137 |
Number of coins that Jane and Fiona gave away
= 193 - 137
= 56
1 p + 4 u = 56
1 p = 56 - 4 u --- (1)
1 p + 4 u + 9 u = 137
1 p + 13 u = 137
1 p = 137 - 13 u --- (2)
(1) = (2)
56 - 4 u = 137 - 13 u
13 u - 4 u = 137 - 56
9 u = 81
1 u = 81 ÷ 9 = 9
From (1)
1 p = 56 - 4 u
1 p = 56 - 4 x 9
1 p = 56 - 36 = 20
Number of coins that Jane and Fiona had at first
= 2 p + 8 u
= 2 x 20 + 8 x 9
= 40 + 81
= 121
Answer(s): 121
