Esther and Tammy have some money. If Esther spends $3, she will have
25 as much money as Tammy. If Tammy spends $21, Esther will have
78 as much money as Tammy. How much money does Tammy have?
| |
Case 1 |
Case 2 |
| |
Esther |
Tammy |
Esther |
Tammy |
| Before |
2 u + $3 |
5 u |
7 p |
8 p + $21 |
| Change |
- $3 |
|
|
- $21 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Esther has at first in Case 1 and Case 2 is the same.
2 u + 3 = 7 p
2 u = 7 p - 3 --- (1)
The amount that Tammy has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 21 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 15 --- (3)
(2)
x 210 u = 16 p + 42 --- (4)
(3) = (4)
35 p - 15 = 16 p + 42
35 p - 16 p = 15 + 42
19 p = 57
1 p = 57 ÷ 19 = 3
Amount that Tammy has
= 8 p + 21
= 8 x 3 + 21
= 24 + 21
= $45
Answer(s): $45
