The ratio of Kylie's money to Usha's money was 1 : 3. After Kylie spent thrice as much as Usha, Kylie and Usha had $9 and $43 left respectively. Find the amount of money each of the girls have at first.
- Kylie
- Usha
|
Make u the same (1)x3 = (3) |
Kylie (1) |
Usha (2) |
Before |
3 u |
1 u |
3 u |
Change |
- 9 p |
- 3 p |
- 1 p |
After |
27 |
9 |
43 |
(a)
1 u - 3 p = 9
3 u = 9 + 3 p --- (1)
3 u - 1 p = 43
3 u = 43 + 1 p --- (2)
(1)
x3
3 u = 27 + 9 p --- (3)
(3) = (2)
27 + 9 p = 43 + 1 p
9 p - 1 p = 43 - 27
8 p = 16
1 p = 16 ÷ 8 = 2
Amount that Kylie had at first
= 9 + 3 p
= 9 + 3 x 2
= 9 + 6
= $15
(b)
Amount that Usha had at first
= 27 + 9 p
= 27 + 9 x 2
= 27 + 18
= $45
Answer(s): (a) $15; (b) $45