Three women, Shiyun, Tiffany and Dana went on a shopping spree. 70% of Shiyun's spending was equal to
12 of Tiffany's spending. Dana's spending was 70% less than Tiffany's. If Tiffany spent $2156 less, she would spend the same amount of money as Dana.
- Find the ratio of Shiyun's spending to Tiffany's to Dana's.
- How much did Dana spend?
Shiyun |
Tiffany |
Dana |
5x10 |
7x10 |
|
|
10x7 |
3x7 |
50 u |
70 u |
21 u |
(a)
70%=
70100 =
710 710 of Shiyun's spending is equal to
12 of Tiffany's spending. Make the numerators the same. LCM of 7 and 1 is 7.
710 of Shiyun's spending =
12 of Tiffany's spending
710 of Shiyun's spending =
1x72x7 of Tiffany's spending
710 of Shiyun's spending =
714 of Tiffany's spending
Shiyun : Tiffany
10 : 14
5 : 7
Dana's spending in percent when compared to Tiffany's
= 100% - 70%
= 30%
Tiffany : Dana
100 : 30
10 : 3
Tiffany's spending is the repeated identity. Make Tiffany's spending the same. LCM of 7 and 10 is 70.
Shiyun : Tiffany : Dana
50 : 70 : 21
(b)
|
Shiyun |
Tiffany |
Dana |
Before |
50 u |
70 u |
21 u |
Change |
|
- 49 u |
|
After |
50 u |
21 u |
21 u |
Additional amount that Tiffany would have to spend less to be the same as Dana
= 70 u - 21 u
= 49 u
49 u = 2156
1 u = 2156 ÷ 49 = 44
Amount that Dana spent
= 21 u
= 21 x 44
= $924
Answer(s): (a) 50 : 70 : 21; (b) $924