The ratio of the amount of money that Lucy and Opal brought along was 4 : 5. For their cousin's present, Lucy and Opal shared the cost in the ratio of 2 : 3. Lucy used up
25 of her money to pay for her share. After paying for her share, Opal had $169 left. How much was the present?
| |
Lucy |
Opal |
| Before |
4 u |
5 u |
| Change |
- 1.6 u |
- 2.4 u |
Comparing the cost shared
between Lucy and Opal |
- 2 p =
- 1.6 u |
- 3 p =
- 2.4 u |
| After |
2.4 u |
169 |
Amount that Lucy spent on the present
=
25 x 4 u
= 1.6 u
2 p = 1.6 u
1 p = 1.6 u ÷ 2 = 0.8
3 p = 3 x 0.8 = 2.4 u
Amount that Opal had left
= 5 u - 2.4 u
= 2.6 u
2.6 u = 169
1 u = 169 ÷ 2.6 = 65
Cost of the present
= 1.6 u + 2.4 u
= 4 u
= 4 x 65
= $260
Answer: $260
