Natalie and Gabby have some money. If Natalie spends $10, she will have
25 as much money as Gabby. If Gabby spends $1, Natalie will have
56 as much money as Gabby. How much money does Gabby have?
| |
Case 1 |
Case 2 |
| |
Natalie |
Gabby |
Natalie |
Gabby |
| Before |
2 u + $10 |
5 u |
5 p |
6 p + $1 |
| Change |
- $10 |
|
|
- $1 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Natalie has at first in Case 1 and Case 2 is the same.
2 u + 10 = 5 p
2 u = 5 p - 10 --- (1)
The amount that Gabby has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 1 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 50 --- (3)
(2)
x 210 u = 12 p + 2 --- (4)
(3) = (4)
25 p - 50 = 12 p + 2
25 p - 12 p = 50 + 2
13 p = 52
1 p = 52 ÷ 13 = 4
Amount that Gabby has
= 6 p + 1
= 6 x 4 + 1
= 24 + 1
= $25
Answer(s): $25
