The ratio of Yen's money to Nora's money was 1 : 3. After Yen spent thrice as much as Nora, Yen and Nora had $4 and $52 left respectively. Find the amount of money each of the girls have at first.
- Yen
- Nora
| |
Make u the same
(1)x3 = (3) |
Yen
(1) |
Nora
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
12 |
4 |
52 |
(a)
1 u - 3 p = 4
3 u = 4 + 3 p --- (1)
3 u - 1 p = 52
3 u = 52 + 1 p --- (2)
(1)
x3
3 u = 12 + 9 p --- (3)
(3) = (2)
12 + 9 p = 52 + 1 p
9 p - 1 p = 52 - 12
8 p = 40
1 p = 40 ÷ 8 = 5
Amount that Yen had at first
= 4 + 3 p
= 4 + 3 x 5
= 4 + 15
= $19
(b)
Amount that Nora had at first
= 12 + 9 p
= 12 + 9 x 5
= 12 + 45
= $57
Answer(s): (a) $19; (b) $57
