Three women, Betty, Joelle and Nicole went on a shopping spree. 30% of Betty's spending was equal to
12 of Joelle's spending. Nicole's spending was 60% more than Joelle's. If Joelle spent another $1026, she would spend the same amount of money as Nicole.
- Find the ratio of Betty's spending to Joelle's to Nicole's.
- How much did Betty spend?
Betty |
Joelle |
Nicole |
5x5 |
3x5 |
|
|
5x3 |
8x3 |
25 u |
15 u |
24 u |
(a)
30%=
30100 =
310 310 of Betty's spending is equal to
12 of Joelle's spending. Make the numerators the same. LCM of 3 and 1 is 3.
310 of Betty's spending =
12 of Joelle's spending
310 of Betty's spending =
1x32x3 of Joelle's spending
310 of Betty's spending =
36 of Joelle's spending
Betty : Joelle
10 : 6
5 : 3
Nicole's spending in percent when compared to Joelle's
= 100% + 60%
= 160%
Joelle : Nicole
100 : 160
5 : 8
Joelle's spending is the repeated identity. Make Joelle's spending the same. LCM of 3 and 5 is 15.
Betty : Joelle : Nicole
25 : 15 : 24
(b)
|
Betty |
Joelle |
Nicole |
Before |
25 u |
15 u |
24 u |
Change |
|
+ 9 u |
|
After |
25 u |
24 u |
24 u |
Additional amount that Joelle would have to spend to be the same as Nicole
= 24 u - 15 u
= 9 u
9 u = 1026
1 u = 1026 ÷ 9 = 114
Amount that Betty spent
= 25 u
= 25 x 114
= $2850
Answer(s): (a) 25 : 15 : 24; (b) $2850