Zara and Sarah have some money. If Zara spends $18, she will have
35 as much money as Sarah. If Sarah spends $6, Zara will have
67 as much money as Sarah. How much money does Sarah have?
| |
Case 1 |
Case 2 |
| |
Zara |
Sarah |
Zara |
Sarah |
| Before |
3 u + $18 |
5 u |
6 p |
7 p + $6 |
| Change |
- $18 |
|
|
- $6 |
| After |
3 u |
5 u |
6 p |
7 p |
The amount that Zara has at first in Case 1 and Case 2 is the same.
3 u + 18 = 6 p
3 u = 6 p - 18 --- (1)
The amount that Sarah has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 6 --- (2)
Make u the same.
(1)
x 515 u = 30 p - 90 --- (3)
(2)
x 315 u = 21 p + 18 --- (4)
(3) = (4)
30 p - 90 = 21 p + 18
30 p - 21 p = 90 + 18
9 p = 108
1 p = 108 ÷ 9 = 12
Amount that Sarah has
= 7 p + 6
= 7 x 12 + 6
= 84 + 6
= $90
Answer(s): $90
