Lucy and Rachel went shopping. After Lucy spent $81
q, Rachel had 4 times as much as Lucy. If Lucy had $24
q more than Rachel at first,
- Express the amount of money that Lucy had at first in terms of q.
- If q = 32, find the amount of money that the two women had left after shopping.
|
Lucy |
Rachel |
Before |
1 u + $81q |
4 u |
Change |
- $81q |
|
After |
1 u |
4 u |
(a)
1 u + 81
q = 4 u + 24
q4 u - 1 u = 81
q - 24
q3 u = 81
q - 24
q = 57
q1 u = 57
q ÷ 3 = 19
q Lucy's amount at first
= 1 u + 81
q = 19
q + 81
q = $100
q (b)
1 u + 4 u = 5 u
5 u = 5 x 19
q = 95
q Amount the two women had left
= 95 x 32
= $3040
Answer(s): (a) $100
q; (b) $3040