Nora and Eva have some money. If Nora spends $18, she will have
35 as much money as Eva. If Eva spends $3, Nora will have
67 as much money as Eva. How much money does Eva have?
| |
Case 1 |
Case 2 |
| |
Nora |
Eva |
Nora |
Eva |
| Before |
3 u + $18 |
5 u |
6 p |
7 p + $3 |
| Change |
- $18 |
|
|
- $3 |
| After |
3 u |
5 u |
6 p |
7 p |
The amount that Nora 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 Eva has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 3 --- (2)
Make u the same.
(1)
x 515 u = 30 p - 90 --- (3)
(2)
x 315 u = 21 p + 9 --- (4)
(3) = (4)
30 p - 90 = 21 p + 9
30 p - 21 p = 90 + 9
9 p = 99
1 p = 99 ÷ 9 = 11
Amount that Eva has
= 7 p + 3
= 7 x 11 + 3
= 77 + 3
= $80
Answer(s): $80
