The ratio of the amount of money that Sarah and Gwen brought along was 4 : 5. For their sister's present, Sarah and Gwen shared the cost in the ratio of 3 : 2. Sarah used up
35 of her money to pay for her share. After paying for her share, Gwen had $255 left. How much was the present?
| |
Sarah |
Gwen |
| Before |
4 u |
5 u |
| Change |
- 2.4 u |
- 1.6 u |
Comparing the cost shared
between Sarah and Gwen |
- 3 p =
- 2.4 u |
- 2 p =
- 1.6 u |
| After |
1.6 u |
255 |
Amount that Sarah spent on the present
=
35 x 4 u
= 2.4 u
3 p = 2.4 u
1 p = 2.4 u ÷ 3 = 0.8
2 p = 2 x 0.8 = 1.6 u
Amount that Gwen had left
= 5 u - 1.6 u
= 3.4 u
3.4 u = 255
1 u = 255 ÷ 3.4 = 75
Cost of the present
= 2.4 u + 1.6 u
= 4 u
= 4 x 75
= $300
Answer: $300
