The ratio of Zara's money to Penelope's money was 1 : 2. After Zara spent thrice as much as Penelope, Zara and Penelope had $8 and $46 left respectively. Find the amount of money each of the girls have at first.
- Zara
- Penelope
| |
Make u the same
(1)x2 = (3) |
Zara
(1) |
Penelope
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
16 |
8 |
46 |
(a)
1 u - 3 p = 8
2 u = 8 + 3 p --- (1)
2 u - 1 p = 46
2 u = 46 + 1 p --- (2)
(1)
x2
2 u = 16 + 6 p --- (3)
(3) = (2)
16 + 6 p = 46 + 1 p
6 p - 1 p = 46 - 16
5 p = 30
1 p = 30 ÷ 5 = 6
Amount that Zara had at first
= 8 + 3 p
= 8 + 3 x 6
= 8 + 18
= $26
(b)
Amount that Penelope had at first
= 16 + 6 p
= 16 + 6 x 6
= 16 + 36
= $52
Answer(s): (a) $26; (b) $52
