Yoko and Emma have some money. If Yoko spends $1, she will have
25 as much money as Emma. If Emma spends $45, Yoko will have
78 as much money as Emma. How much money does Emma have?
| |
Case 1 |
Case 2 |
| |
Yoko |
Emma |
Yoko |
Emma |
| Before |
2 u + $1 |
5 u |
7 p |
8 p + $45 |
| Change |
- $1 |
|
|
- $45 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Yoko has at first in Case 1 and Case 2 is the same.
2 u + 1 = 7 p
2 u = 7 p - 1 --- (1)
The amount that Emma has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 45 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 5 --- (3)
(2)
x 210 u = 16 p + 90 --- (4)
(3) = (4)
35 p - 5 = 16 p + 90
35 p - 16 p = 5 + 90
19 p = 95
1 p = 95 ÷ 19 = 5
Amount that Emma has
= 8 p + 45
= 8 x 5 + 45
= 40 + 45
= $85
Answer(s): $85
