Three women, Mary, Pamela and Sarah went on a shopping spree. 90% of Mary's spending was equal to
16 of Pamela's spending. Sarah's spending was 25% less than Pamela's. If Pamela spent $810 less, she would spend the same amount of money as Sarah.
- Find the ratio of Mary's spending to Pamela's to Sarah's.
- How much did Sarah spend?
Mary |
Pamela |
Sarah |
5x4 |
27x4 |
|
|
4x27 |
3x27 |
20 u |
108 u |
81 u |
(a)
90%=
90100 =
910 910 of Mary's spending is equal to
16 of Pamela's spending. Make the numerators the same. LCM of 9 and 1 is 9.
910 of Mary's spending =
16 of Pamela's spending
910 of Mary's spending =
1x96x9 of Pamela's spending
910 of Mary's spending =
954 of Pamela's spending
Mary : Pamela
10 : 54
5 : 27
Sarah's spending in percent when compared to Pamela's
= 100% - 25%
= 75%
Pamela : Sarah
100 : 75
4 : 3
Pamela's spending is the repeated identity. Make Pamela's spending the same. LCM of 27 and 4 is 108.
Mary : Pamela : Sarah
20 : 108 : 81
(b)
|
Mary |
Pamela |
Sarah |
Before |
20 u |
108 u |
81 u |
Change |
|
- 27 u |
|
After |
20 u |
81 u |
81 u |
Additional amount that Pamela would have to spend less to be the same as Sarah
= 108 u - 81 u
= 27 u
27 u = 810
1 u = 810 ÷ 27 = 30
Amount that Sarah spent
= 81 u
= 81 x 30
= $2430
Answer(s): (a) 20 : 108 : 81; (b) $2430