The ratio of the amount of money that Barbara and Betty brought along was 4 : 5. For their brother's gift, Barbara and Betty shared the cost in the ratio of 3 : 2. Barbara used up
35 of her money to pay for her share. After paying for her share, Betty had $153 left. How much was the gift?
| |
Barbara |
Betty |
| Before |
4 u |
5 u |
| Change |
- 2.4 u |
- 1.6 u |
Comparing the cost shared
between Barbara and Betty |
- 3 p =
- 2.4 u |
- 2 p =
- 1.6 u |
| After |
1.6 u |
153 |
Amount that Barbara spent on the gift
=
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 Betty had left
= 5 u - 1.6 u
= 3.4 u
3.4 u = 153
1 u = 153 ÷ 3.4 = 45
Cost of the gift
= 2.4 u + 1.6 u
= 4 u
= 4 x 45
= $180
Answer: $180
