The ratio of Barbara's money to Xylia's money was 1 : 4. After Barbara spent thrice as much as Xylia, Barbara and Xylia had $5 and $53 left respectively. Find the amount of money each of the girls have at first.
- Barbara
- Xylia
| |
Make u the same
(1)x4 = (3) |
Barbara
(1) |
Xylia
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 12 p |
- 3 p |
- 1 p |
| After |
20 |
5 |
53 |
(a)
1 u - 3 p = 5
4 u = 5 + 3 p --- (1)
4 u - 1 p = 53
4 u = 53 + 1 p --- (2)
(1)
x4
4 u = 20 + 12 p --- (3)
(3) = (2)
20 + 12 p = 53 + 1 p
12 p - 1 p = 53 - 20
11 p = 33
1 p = 33 ÷ 11 = 3
Amount that Barbara had at first
= 5 + 3 p
= 5 + 3 x 3
= 5 + 9
= $14
(b)
Amount that Xylia had at first
= 20 + 12 p
= 20 + 12 x 3
= 20 + 36
= $56
Answer(s): (a) $14; (b) $56
