The ratio of Penelope's money to Tina's money was 1 : 2. After Penelope spent thrice as much as Tina, Penelope and Tina had $6 and $37 left respectively. Find the amount of money each of the girls have at first.
- Penelope
- Tina
| |
Make u the same
(1)x2 = (3) |
Penelope
(1) |
Tina
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
12 |
6 |
37 |
(a)
1 u - 3 p = 6
2 u = 6 + 3 p --- (1)
2 u - 1 p = 37
2 u = 37 + 1 p --- (2)
(1)
x2
2 u = 12 + 6 p --- (3)
(3) = (2)
12 + 6 p = 37 + 1 p
6 p - 1 p = 37 - 12
5 p = 25
1 p = 25 ÷ 5 = 5
Amount that Penelope had at first
= 6 + 3 p
= 6 + 3 x 5
= 6 + 15
= $21
(b)
Amount that Tina had at first
= 12 + 6 p
= 12 + 6 x 5
= 12 + 30
= $42
Answer(s): (a) $21; (b) $42
