The ratio of the amount of money that Lucy and Xuan brought along was 3 : 4. For their brother's gift, Lucy and Xuan shared the cost in the ratio of 3 : 2. Lucy used up
35 of her money to pay for her share. After paying for her share, Xuan had $224 left. How much was the gift?
|
Lucy |
Xuan |
Before |
3 u |
4 u |
Change |
- 1.8 u |
- 1.2 u |
Comparing the cost shared between Lucy and Xuan |
- 3 p = - 1.8 u |
- 2 p = - 1.2 u |
After |
1.2 u |
224 |
Amount that Lucy spent on the gift
=
35 x 3 u
= 1.8 u
3 p = 1.8 u
1 p = 1.8 u ÷ 3 = 0.6
2 p = 2 x 0.6 = 1.2 u
Amount that Xuan had left
= 4 u - 1.2 u
= 2.8 u
2.8 u = 224
1 u = 224 ÷ 2.8 = 80
Cost of the gift
= 1.8 u + 1.2 u
= 3 u
= 3 x 80
= $240
Answer: $240