Yen and Gem have some money. If Yen spends $10, she will have
25 as much money as Gem. If Gem spends $11, Yen will have
58 as much money as Gem. How much money does Yen have?
| |
Case 1 |
Case 2 |
| |
Yen |
Gem |
Yen |
Gem |
| Before |
2 u + $10 |
5 u |
5 p |
8 p + $11 |
| Change |
- $10 |
|
|
- $11 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Yen has at first in Case 1 and Case 2 is the same.
2 u + 10 = 5 p
2 u = 5 p - 10 --- (1)
The amount that Gem has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 11 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 50 --- (3)
(2)
x 210 u = 16 p + 22 --- (4)
(3) = (4)
25 p - 50 = 16 p + 22
25 p - 16 p = 50 + 22
9 p = 72
1 p = 72 ÷ 9 = 8
Amount that Yen has
= 5 p
= 5 x 8
= $40
Answer(s): $40
