The ratio of Tammy's money to Rachel's money was 1 : 3. After Tammy spent thrice as much as Rachel, Tammy and Rachel had $8 and $56 left respectively. Find the amount of money each of the girls have at first.
- Tammy
- Rachel
| |
Make u the same
(1)x3 = (3) |
Tammy
(1) |
Rachel
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
24 |
8 |
56 |
(a)
1 u - 3 p = 8
3 u = 8 + 3 p --- (1)
3 u - 1 p = 56
3 u = 56 + 1 p --- (2)
(1)
x3
3 u = 24 + 9 p --- (3)
(3) = (2)
24 + 9 p = 56 + 1 p
9 p - 1 p = 56 - 24
8 p = 32
1 p = 32 ÷ 8 = 4
Amount that Tammy had at first
= 8 + 3 p
= 8 + 3 x 4
= 8 + 12
= $20
(b)
Amount that Rachel had at first
= 24 + 9 p
= 24 + 9 x 4
= 24 + 36
= $60
Answer(s): (a) $20; (b) $60
