Lynn and Emily have some money. If Lynn spends $4, she will have
45 as much money as Emily. If Emily spends $2, Lynn will have
67 as much money as Emily. How much money does Emily have?
| |
Case 1 |
Case 2 |
| |
Lynn |
Emily |
Lynn |
Emily |
| Before |
4 u + $4 |
5 u |
6 p |
7 p + $2 |
| Change |
- $4 |
|
|
- $2 |
| After |
4 u |
5 u |
6 p |
7 p |
The amount that Lynn has at first in Case 1 and Case 2 is the same.
4 u + 4 = 6 p
4 u = 6 p - 4 --- (1)
The amount that Emily has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 2 --- (2)
Make u the same.
(1)
x 520 u = 30 p - 20 --- (3)
(2)
x 420 u = 28 p + 8 --- (4)
(3) = (4)
30 p - 20 = 28 p + 8
30 p - 28 p = 20 + 8
2 p = 28
1 p = 28 ÷ 2 = 14
Amount that Emily has
= 7 p + 2
= 7 x 14 + 2
= 98 + 2
= $100
Answer(s): $100
