The ratio of Barbara's money to Kylie's money was 1 : 2. After Barbara spent five times as much as Kylie, Barbara and Kylie had $9 and $36 left respectively. Find the amount of money each of the girls have at first.
- Barbara
- Kylie
| |
Make u the same
(1)x2 = (3) |
Barbara
(1) |
Kylie
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
18 |
9 |
36 |
(a)
1 u - 5 p = 9
2 u = 9 + 5 p --- (1)
2 u - 1 p = 36
2 u = 36 + 1 p --- (2)
(1)
x2
2 u = 18 + 10 p --- (3)
(3) = (2)
18 + 10 p = 36 + 1 p
10 p - 1 p = 36 - 18
9 p = 18
1 p = 18 ÷ 9 = 2
Amount that Barbara had at first
= 9 + 5 p
= 9 + 5 x 2
= 9 + 10
= $19
(b)
Amount that Kylie had at first
= 18 + 10 p
= 18 + 10 x 2
= 18 + 20
= $38
Answer(s): (a) $19; (b) $38
