The ratio of Tina's money to Diana's money was 1 : 5. After Tina spent thrice as much as Diana, Tina and Diana had $4 and $48 left respectively. Find the amount of money each of the girls have at first.
- Tina
- Diana
| |
Make u the same
(1)x5 = (3) |
Tina
(1) |
Diana
(2) |
| Before |
5 u |
1 u |
5 u |
| Change |
- 15 p |
- 3 p |
- 1 p |
| After |
20 |
4 |
48 |
(a)
1 u - 3 p = 4
5 u = 4 + 3 p --- (1)
5 u - 1 p = 48
5 u = 48 + 1 p --- (2)
(1)
x5
5 u = 20 + 15 p --- (3)
(3) = (2)
20 + 15 p = 48 + 1 p
15 p - 1 p = 48 - 20
14 p = 28
1 p = 28 ÷ 14 = 2
Amount that Tina had at first
= 4 + 3 p
= 4 + 3 x 2
= 4 + 6
= $10
(b)
Amount that Diana had at first
= 20 + 15 p
= 20 + 15 x 2
= 20 + 30
= $50
Answer(s): (a) $10; (b) $50
