Vanessa and Diana went shopping. After Vanessa spent $72
d, Diana had 4 times as much as Vanessa. If Vanessa had $30
d more than Diana at first,
- Express the amount of money that Vanessa had at first in terms of d.
- If d = 22, find the amount of money that the two women had left after shopping.
|
Vanessa |
Diana |
Before |
1 u + $72d |
4 u |
Change |
- $72d |
|
After |
1 u |
4 u |
(a)
1 u + 72
d = 4 u + 30
d4 u - 1 u = 72
d - 30
d3 u = 72
d - 30
d = 42
d1 u = 42
d ÷ 3 = 14
d Vanessa's amount at first
= 1 u + 72
d = 14
d + 72
d = $86
d (b)
1 u + 4 u = 5 u
5 u = 5 x 14
d = 70
d Amount the two women had left
= 70 x 22
= $1540
Answer(s): (a) $86
d; (b) $1540