Three women, Marion, Olivia and Linda went on a shopping spree. 30% of Marion's spending was equal to
12 of Olivia's spending. Linda's spending was 40% more than Olivia's. If Olivia spent another $618, she would spend the same amount of money as Linda.
- Find the ratio of Marion's spending to Olivia's to Linda's.
- How much did Marion spend?
Marion |
Olivia |
Linda |
5x5 |
3x5 |
|
|
5x3 |
7x3 |
25 u |
15 u |
21 u |
(a)
30%=
30100 =
310 310 of Marion's spending is equal to
12 of Olivia's spending. Make the numerators the same. LCM of 3 and 1 is 3.
310 of Marion's spending =
12 of Olivia's spending
310 of Marion's spending =
1x32x3 of Olivia's spending
310 of Marion's spending =
36 of Olivia's spending
Marion : Olivia
10 : 6
5 : 3
Linda's spending in percent when compared to Olivia's
= 100% + 40%
= 140%
Olivia : Linda
100 : 140
5 : 7
Olivia's spending is the repeated identity. Make Olivia's spending the same. LCM of 3 and 5 is 15.
Marion : Olivia : Linda
25 : 15 : 21
(b)
|
Marion |
Olivia |
Linda |
Before |
25 u |
15 u |
21 u |
Change |
|
+ 6 u |
|
After |
25 u |
21 u |
21 u |
Additional amount that Olivia would have to spend to be the same as Linda
= 21 u - 15 u
= 6 u
6 u = 618
1 u = 618 ÷ 6 = 103
Amount that Marion spent
= 25 u
= 25 x 103
= $2575
Answer(s): (a) 25 : 15 : 21; (b) $2575