Zara and Dana have some money. If Zara spends $6, she will have
34 as much money as Dana. If Dana spends $2, Zara will have
67 as much money as Dana. How much money does Dana have?
| |
Case 1 |
Case 2 |
| |
Zara |
Dana |
Zara |
Dana |
| Before |
3 u + $6 |
4 u |
6 p |
7 p + $2 |
| Change |
- $6 |
|
|
- $2 |
| After |
3 u |
4 u |
6 p |
7 p |
The amount that Zara has at first in Case 1 and Case 2 is the same.
3 u + 6 = 6 p
3 u = 6 p - 6 --- (1)
The amount that Dana has at first in Case 1 and Case 2 is the same.
4 u = 7 p + 2 --- (2)
Make u the same.
(1)
x 412 u = 24 p - 24 --- (3)
(2)
x 312 u = 21 p + 6 --- (4)
(3) = (4)
24 p - 24 = 21 p + 6
24 p - 21 p = 24 + 6
3 p = 30
1 p = 30 ÷ 3 = 10
Amount that Dana has
= 7 p + 2
= 7 x 10 + 2
= 70 + 2
= $72
Answer(s): $72
