The ratio of Penelope's money to Victoria's money was 1 : 4. After Penelope spent thrice as much as Victoria, Penelope and Victoria had $9 and $58 left respectively. Find the amount of money each of the girls have at first.
- Penelope
- Victoria
| |
Make u the same
(1)x4 = (3) |
Penelope
(1) |
Victoria
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 12 p |
- 3 p |
- 1 p |
| After |
36 |
9 |
58 |
(a)
1 u - 3 p = 9
4 u = 9 + 3 p --- (1)
4 u - 1 p = 58
4 u = 58 + 1 p --- (2)
(1)
x4
4 u = 36 + 12 p --- (3)
(3) = (2)
36 + 12 p = 58 + 1 p
12 p - 1 p = 58 - 36
11 p = 22
1 p = 22 ÷ 11 = 2
Amount that Penelope had at first
= 9 + 3 p
= 9 + 3 x 2
= 9 + 6
= $15
(b)
Amount that Victoria had at first
= 36 + 12 p
= 36 + 12 x 2
= 36 + 24
= $60
Answer(s): (a) $15; (b) $60
