The ratio of Diana's money to Xandra's money was 1 : 3. After Diana spent four times as much as Xandra, Diana and Xandra had $6 and $51 left respectively. Find the amount of money each of the girls have at first.
- Diana
- Xandra
| |
Make u the same
(1)x3 = (3) |
Diana
(1) |
Xandra
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 12 p |
- 4 p |
- 1 p |
| After |
18 |
6 |
51 |
(a)
1 u - 4 p = 6
3 u = 6 + 4 p --- (1)
3 u - 1 p = 51
3 u = 51 + 1 p --- (2)
(1)
x3
3 u = 18 + 12 p --- (3)
(3) = (2)
18 + 12 p = 51 + 1 p
12 p - 1 p = 51 - 18
11 p = 33
1 p = 33 ÷ 11 = 3
Amount that Diana had at first
= 6 + 4 p
= 6 + 4 x 3
= 6 + 12
= $18
(b)
Amount that Xandra had at first
= 18 + 12 p
= 18 + 12 x 3
= 18 + 36
= $54
Answer(s): (a) $18; (b) $54
