Rachel and Barbara went shopping. After Rachel spent $52
y, Barbara had 5 times as much as Rachel. If Rachel had $24
y more than Barbara at first,
- Express the amount of money that Rachel had at first in terms of y.
- If y = 34, find the amount of money that the two women had left after shopping.
|
Rachel |
Barbara |
Before |
1 u + $52y |
5 u |
Change |
- $52y |
|
After |
1 u |
5 u |
(a)
1 u + 52
y = 5 u + 24
y5 u - 1 u = 52
y - 24
y4 u = 52
y - 24
y = 28
y1 u = 28
y ÷ 4 = 7
y Rachel's amount at first
= 1 u + 52
y = 7
y + 52
y = $59
y (b)
1 u + 5 u = 6 u
6 u = 6 x 7
y = 42
y Amount the two women had left
= 42 x 34
= $1428
Answer(s): (a) $59
y; (b) $1428