PSLEMary and Gillian went shopping together with a total amount of $101.40. Mary spent 2 times as much as Gillian. The amount Gillian had left was $31 more than what she had spent. She had 2 times as much money left as Mary.
(a) How much money did Gillian spend?
(b) How much money did Mary have at first?
|
Mary |
Gillian |
Total |
Before |
2.5 u + 15.5 |
2 u + 31 |
101.40 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 15.5 |
1 u + 31 |
|
(a)
Total amount that Mary and Gillian had at first
= (2.5 u + 15.5) + (2 u + 31)
= 2.5 u + 2 u + 15.5 + 31
= 4.5 u + 46.5
4.5 u + 46.5 = 101.4
4.5 u = 101.4 - 46.5
4.5 u = 54.9
1 u = 54.9 ÷ 4.5 = 12.2
Amount that Gillian had at first
= 1 u
= $12.20
(b)
Amount that Mary had at first
= 2.5 u + 15.5
= (2.5 x 12.2) + 15.5
= 30.5 + 15.5
= $46
Answer(s): (a) $12.20; (b) $46