The ratio of Victoria's money to Emily's money was 1 : 2. After Victoria spent thrice as much as Emily, Victoria and Emily had $5 and $55 left respectively. Find the amount of money each of the girls have at first.
- Victoria
- Emily
| |
Make u the same
(1)x2 = (3) |
Victoria
(1) |
Emily
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
10 |
5 |
55 |
(a)
1 u - 3 p = 5
2 u = 5 + 3 p --- (1)
2 u - 1 p = 55
2 u = 55 + 1 p --- (2)
(1)
x2
2 u = 10 + 6 p --- (3)
(3) = (2)
10 + 6 p = 55 + 1 p
6 p - 1 p = 55 - 10
5 p = 45
1 p = 45 ÷ 5 = 9
Amount that Victoria had at first
= 5 + 3 p
= 5 + 3 x 9
= 5 + 27
= $32
(b)
Amount that Emily had at first
= 10 + 6 p
= 10 + 6 x 9
= 10 + 54
= $64
Answer(s): (a) $32; (b) $64
