Jade and Olivia have some money. If Jade spends $24, she will have
25 as much money as Olivia. If Olivia spends $16, Jade will have
78 as much money as Olivia. How much money does Jade have?
| |
Case 1 |
Case 2 |
| |
Jade |
Olivia |
Jade |
Olivia |
| Before |
2 u + $24 |
5 u |
7 p |
8 p + $16 |
| Change |
- $24 |
|
|
- $16 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Jade has at first in Case 1 and Case 2 is the same.
2 u + 24 = 7 p
2 u = 7 p - 24 --- (1)
The amount that Olivia has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 16 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 120 --- (3)
(2)
x 210 u = 16 p + 32 --- (4)
(3) = (4)
35 p - 120 = 16 p + 32
35 p - 16 p = 120 + 32
19 p = 152
1 p = 152 ÷ 19 = 8
Amount that Jade has
= 7 p
= 7 x 8
= $56
Answer(s): $56
