The ratio of Cathy's money to Natalie's money was 1 : 2. After Cathy spent five times as much as Natalie, Cathy and Natalie had $8 and $43 left respectively. Find the amount of money each of the girls have at first.
- Cathy
- Natalie
| |
Make u the same
(1)x2 = (3) |
Cathy
(1) |
Natalie
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
16 |
8 |
43 |
(a)
1 u - 5 p = 8
2 u = 8 + 5 p --- (1)
2 u - 1 p = 43
2 u = 43 + 1 p --- (2)
(1)
x2
2 u = 16 + 10 p --- (3)
(3) = (2)
16 + 10 p = 43 + 1 p
10 p - 1 p = 43 - 16
9 p = 27
1 p = 27 ÷ 9 = 3
Amount that Cathy had at first
= 8 + 5 p
= 8 + 5 x 3
= 8 + 15
= $23
(b)
Amount that Natalie had at first
= 16 + 10 p
= 16 + 10 x 3
= 16 + 30
= $46
Answer(s): (a) $23; (b) $46
