The ratio of the amount of money that Olivia and Natalie brought along was 4 : 5. For their brother's souvenir, Olivia and Natalie shared the cost in the ratio of 2 : 3. Olivia used up
25 of her money to pay for her share. After paying for her share, Natalie had $130 left. How much was the souvenir?
|
Olivia |
Natalie |
Before |
4 u |
5 u |
Change |
- 1.6 u |
- 2.4 u |
Comparing the cost shared between Olivia and Natalie |
- 2 p = - 1.6 u |
- 3 p = - 2.4 u |
After |
2.4 u |
130 |
Amount that Olivia spent on the souvenir
=
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 Natalie had left
= 5 u - 2.4 u
= 2.6 u
2.6 u = 130
1 u = 130 ÷ 2.6 = 50
Cost of the souvenir
= 1.6 u + 2.4 u
= 4 u
= 4 x 50
= $200
Answer: $200