PSLEDana and Ivory went shopping together with a total amount of $83.40. Dana spent 2 times as much as Ivory. The amount Ivory had left was $7 more than what she had spent. She had 2 times as much money left as Dana.
(a) How much money did Ivory spend?
(b) How much money did Dana have at first?
|
Dana |
Ivory |
Total |
Before |
2.5 u + 3.5 |
2 u + 7 |
83.40 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 3.5 |
1 u + 7 |
|
(a)
Total amount that Dana and Ivory had at first
= (2.5 u + 3.5) + (2 u + 7)
= 2.5 u + 2 u + 3.5 + 7
= 4.5 u + 10.5
4.5 u + 10.5 = 83.4
4.5 u = 83.4 - 10.5
4.5 u = 72.9
1 u = 72.9 ÷ 4.5 = 16.2
Amount that Ivory had at first
= 1 u
= $16.20
(b)
Amount that Dana had at first
= 2.5 u + 3.5
= (2.5 x 16.2) + 3.5
= 40.5 + 3.5
= $44
Answer(s): (a) $16.20; (b) $44