PSLEOpal and Raeann went shopping together with a total amount of $109.80. Opal spent 2 times as much as Raeann. The amount Raeann had left was $36 more than what she had spent. She had 2 times as much money left as Opal.
(a) How much money did Raeann spend?
(b) How much money did Opal have at first?
|
Opal |
Raeann |
Total |
Before |
2.5 u + 18 |
2 u + 36 |
109.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 18 |
1 u + 36 |
|
(a)
Total amount that Opal and Raeann had at first
= (2.5 u + 18) + (2 u + 36)
= 2.5 u + 2 u + 18 + 36
= 4.5 u + 54
4.5 u + 54 = 109.8
4.5 u = 109.8 - 54
4.5 u = 55.8
1 u = 55.8 ÷ 4.5 = 12.4
Amount that Raeann had at first
= 1 u
= $12.40
(b)
Amount that Opal had at first
= 2.5 u + 18
= (2.5 x 12.4) + 18
= 31 + 18
= $49
Answer(s): (a) $12.40; (b) $49