The ratio of Dana's money to Zara's money was 1 : 2. After Dana spent thrice as much as Zara, Dana and Zara had $7 and $49 left respectively. Find the amount of money each of the girls have at first.
- Dana
- Zara
| |
Make u the same
(1)x2 = (3) |
Dana
(1) |
Zara
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
14 |
7 |
49 |
(a)
1 u - 3 p = 7
2 u = 7 + 3 p --- (1)
2 u - 1 p = 49
2 u = 49 + 1 p --- (2)
(1)
x2
2 u = 14 + 6 p --- (3)
(3) = (2)
14 + 6 p = 49 + 1 p
6 p - 1 p = 49 - 14
5 p = 35
1 p = 35 ÷ 5 = 7
Amount that Dana had at first
= 7 + 3 p
= 7 + 3 x 7
= 7 + 21
= $28
(b)
Amount that Zara had at first
= 14 + 6 p
= 14 + 6 x 7
= 14 + 42
= $56
Answer(s): (a) $28; (b) $56
