Joelle and Fiona have some money. If Joelle spends $16, she will have
25 as much money as Fiona. If Fiona spends $36, Joelle will have
78 as much money as Fiona. How much money does Fiona have?
| |
Case 1 |
Case 2 |
| |
Joelle |
Fiona |
Joelle |
Fiona |
| Before |
2 u + $16 |
5 u |
7 p |
8 p + $36 |
| Change |
- $16 |
|
|
- $36 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Joelle has at first in Case 1 and Case 2 is the same.
2 u + 16 = 7 p
2 u = 7 p - 16 --- (1)
The amount that Fiona has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 36 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 80 --- (3)
(2)
x 210 u = 16 p + 72 --- (4)
(3) = (4)
35 p - 80 = 16 p + 72
35 p - 16 p = 80 + 72
19 p = 152
1 p = 152 ÷ 19 = 8
Amount that Fiona has
= 8 p + 36
= 8 x 8 + 36
= 64 + 36
= $100
Answer(s): $100
