The ratio of Hazel's money to Olivia's money was 1 : 2. After Hazel spent thrice as much as Olivia, Hazel and Olivia had $5 and $45 left respectively. Find the amount of money each of the girls have at first.
- Hazel
- Olivia
| |
Make u the same
(1)x2 = (3) |
Hazel
(1) |
Olivia
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
10 |
5 |
45 |
(a)
1 u - 3 p = 5
2 u = 5 + 3 p --- (1)
2 u - 1 p = 45
2 u = 45 + 1 p --- (2)
(1)
x2
2 u = 10 + 6 p --- (3)
(3) = (2)
10 + 6 p = 45 + 1 p
6 p - 1 p = 45 - 10
5 p = 35
1 p = 35 ÷ 5 = 7
Amount that Hazel had at first
= 5 + 3 p
= 5 + 3 x 7
= 5 + 21
= $26
(b)
Amount that Olivia had at first
= 10 + 6 p
= 10 + 6 x 7
= 10 + 42
= $52
Answer(s): (a) $26; (b) $52
