PSLEEsther and Yen went shopping together with a total amount of $99.60. Esther spent 2 times as much as Yen. The amount Yen had left was $19 more than what she had spent. She had 2 times as much money left as Esther.
(a) How much money did Yen spend?
(b) How much money did Esther have at first?
|
Esther |
Yen |
Total |
Before |
2.5 u + 9.5 |
2 u + 19 |
99.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 9.5 |
1 u + 19 |
|
(a)
Total amount that Esther and Yen had at first
= (2.5 u + 9.5) + (2 u + 19)
= 2.5 u + 2 u + 9.5 + 19
= 4.5 u + 28.5
4.5 u + 28.5 = 99.6
4.5 u = 99.6 - 28.5
4.5 u = 71.1
1 u = 71.1 ÷ 4.5 = 15.8
Amount that Yen had at first
= 1 u
= $15.80
(b)
Amount that Esther had at first
= 2.5 u + 9.5
= (2.5 x 15.8) + 9.5
= 39.5 + 9.5
= $49
Answer(s): (a) $15.80; (b) $49