The ratio of Anna's money to Kathy's money was 1 : 3. After Anna spent thrice as much as Kathy, Anna and Kathy had $4 and $36 left respectively. Find the amount of money each of the girls have at first.
- Anna
- Kathy
| |
Make u the same
(1)x3 = (3) |
Anna
(1) |
Kathy
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
12 |
4 |
36 |
(a)
1 u - 3 p = 4
3 u = 4 + 3 p --- (1)
3 u - 1 p = 36
3 u = 36 + 1 p --- (2)
(1)
x3
3 u = 12 + 9 p --- (3)
(3) = (2)
12 + 9 p = 36 + 1 p
9 p - 1 p = 36 - 12
8 p = 24
1 p = 24 ÷ 8 = 3
Amount that Anna had at first
= 4 + 3 p
= 4 + 3 x 3
= 4 + 9
= $13
(b)
Amount that Kathy had at first
= 12 + 9 p
= 12 + 9 x 3
= 12 + 27
= $39
Answer(s): (a) $13; (b) $39
