The ratio of Cindy's money to Tammy's money was 1 : 2. After Cindy spent five times as much as Tammy, Cindy and Tammy had $7 and $41 left respectively. Find the amount of money each of the girls have at first.
- Cindy
- Tammy
| |
Make u the same
(1)x2 = (3) |
Cindy
(1) |
Tammy
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
14 |
7 |
41 |
(a)
1 u - 5 p = 7
2 u = 7 + 5 p --- (1)
2 u - 1 p = 41
2 u = 41 + 1 p --- (2)
(1)
x2
2 u = 14 + 10 p --- (3)
(3) = (2)
14 + 10 p = 41 + 1 p
10 p - 1 p = 41 - 14
9 p = 27
1 p = 27 ÷ 9 = 3
Amount that Cindy had at first
= 7 + 5 p
= 7 + 5 x 3
= 7 + 15
= $22
(b)
Amount that Tammy had at first
= 14 + 10 p
= 14 + 10 x 3
= 14 + 30
= $44
Answer(s): (a) $22; (b) $44
