The ratio of Tammy's money to Nora's money was 1 : 2. After Tammy spent thrice as much as Nora, Tammy and Nora had $9 and $53 left respectively. Find the amount of money each of the girls have at first.
- Tammy
- Nora
| |
Make u the same
(1)x2 = (3) |
Tammy
(1) |
Nora
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
18 |
9 |
53 |
(a)
1 u - 3 p = 9
2 u = 9 + 3 p --- (1)
2 u - 1 p = 53
2 u = 53 + 1 p --- (2)
(1)
x2
2 u = 18 + 6 p --- (3)
(3) = (2)
18 + 6 p = 53 + 1 p
6 p - 1 p = 53 - 18
5 p = 35
1 p = 35 ÷ 5 = 7
Amount that Tammy had at first
= 9 + 3 p
= 9 + 3 x 7
= 9 + 21
= $30
(b)
Amount that Nora had at first
= 18 + 6 p
= 18 + 6 x 7
= 18 + 42
= $60
Answer(s): (a) $30; (b) $60
