The ratio of the amount of money that Xandra and Rachel brought along was 3 : 4. For their sister's gift, Xandra and Rachel shared the cost in the ratio of 3 : 2. Xandra used up
35 of her money to pay for her share. After paying for her share, Rachel had $210 left. How much was the gift?
| |
Xandra |
Rachel |
| Before |
3 u |
4 u |
| Change |
- 1.8 u |
- 1.2 u |
Comparing the cost shared
between Xandra and Rachel |
- 3 p =
- 1.8 u |
- 2 p =
- 1.2 u |
| After |
1.2 u |
210 |
Amount that Xandra 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 Rachel had left
= 4 u - 1.2 u
= 2.8 u
2.8 u = 210
1 u = 210 ÷ 2.8 = 75
Cost of the gift
= 1.8 u + 1.2 u
= 3 u
= 3 x 75
= $225
Answer: $225
