The ratio of Anna's money to Diana's money was 1 : 3. After Anna spent thrice as much as Diana, Anna and Diana had $6 and $42 left respectively. Find the amount of money each of the girls have at first.
- Anna
- Diana
| |
Make u the same
(1)x3 = (3) |
Anna
(1) |
Diana
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
18 |
6 |
42 |
(a)
1 u - 3 p = 6
3 u = 6 + 3 p --- (1)
3 u - 1 p = 42
3 u = 42 + 1 p --- (2)
(1)
x3
3 u = 18 + 9 p --- (3)
(3) = (2)
18 + 9 p = 42 + 1 p
9 p - 1 p = 42 - 18
8 p = 24
1 p = 24 ÷ 8 = 3
Amount that Anna had at first
= 6 + 3 p
= 6 + 3 x 3
= 6 + 9
= $15
(b)
Amount that Diana had at first
= 18 + 9 p
= 18 + 9 x 3
= 18 + 27
= $45
Answer(s): (a) $15; (b) $45
