Emma and Usha have some money. If Emma spends $12, she will have
25 as much money as Usha. If Usha spends $14, Emma will have
57 as much money as Usha. How much money does Emma have?
| |
Case 1 |
Case 2 |
| |
Emma |
Usha |
Emma |
Usha |
| Before |
2 u + $12 |
5 u |
5 p |
7 p + $14 |
| Change |
- $12 |
|
|
- $14 |
| After |
2 u |
5 u |
5 p |
7 p |
The amount that Emma has at first in Case 1 and Case 2 is the same.
2 u + 12 = 5 p
2 u = 5 p - 12 --- (1)
The amount that Usha has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 14 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 60 --- (3)
(2)
x 210 u = 14 p + 28 --- (4)
(3) = (4)
25 p - 60 = 14 p + 28
25 p - 14 p = 60 + 28
11 p = 88
1 p = 88 ÷ 11 = 8
Amount that Emma has
= 5 p
= 5 x 8
= $40
Answer(s): $40
