Ivory and Anna have some money. If Ivory spends $12, she will have
35 as much money as Anna. If Anna spends $10, Ivory will have
67 as much money as Anna. How much money does Ivory have?
| |
Case 1 |
Case 2 |
| |
Ivory |
Anna |
Ivory |
Anna |
| Before |
3 u + $12 |
5 u |
6 p |
7 p + $10 |
| Change |
- $12 |
|
|
- $10 |
| After |
3 u |
5 u |
6 p |
7 p |
The amount that Ivory has at first in Case 1 and Case 2 is the same.
3 u + 12 = 6 p
3 u = 6 p - 12 --- (1)
The amount that Anna has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 10 --- (2)
Make u the same.
(1)
x 515 u = 30 p - 60 --- (3)
(2)
x 315 u = 21 p + 30 --- (4)
(3) = (4)
30 p - 60 = 21 p + 30
30 p - 21 p = 60 + 30
9 p = 90
1 p = 90 ÷ 9 = 10
Amount that Ivory has
= 6 p
= 6 x 10
= $60
Answer(s): $60
