Usha and Betty have some money. If Usha spends $5, she will have
25 as much money as Betty. If Betty spends $1, Usha will have
58 as much money as Betty. How much money does Usha have?
| |
Case 1 |
Case 2 |
| |
Usha |
Betty |
Usha |
Betty |
| Before |
2 u + $5 |
5 u |
5 p |
8 p + $1 |
| Change |
- $5 |
|
|
- $1 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Usha has at first in Case 1 and Case 2 is the same.
2 u + 5 = 5 p
2 u = 5 p - 5 --- (1)
The amount that Betty has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 1 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 25 --- (3)
(2)
x 210 u = 16 p + 2 --- (4)
(3) = (4)
25 p - 25 = 16 p + 2
25 p - 16 p = 25 + 2
9 p = 27
1 p = 27 ÷ 9 = 3
Amount that Usha has
= 5 p
= 5 x 3
= $15
Answer(s): $15
