Kylie and Gem have some money. If Kylie spends $17, she will have
25 as much money as Gem. If Gem spends $24, Kylie will have
78 as much money as Gem. How much money does Gem have?
| |
Case 1 |
Case 2 |
| |
Kylie |
Gem |
Kylie |
Gem |
| Before |
2 u + $17 |
5 u |
7 p |
8 p + $24 |
| Change |
- $17 |
|
|
- $24 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Kylie has at first in Case 1 and Case 2 is the same.
2 u + 17 = 7 p
2 u = 7 p - 17 --- (1)
The amount that Gem has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 24 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 85 --- (3)
(2)
x 210 u = 16 p + 48 --- (4)
(3) = (4)
35 p - 85 = 16 p + 48
35 p - 16 p = 85 + 48
19 p = 133
1 p = 133 ÷ 19 = 7
Amount that Gem has
= 8 p + 24
= 8 x 7 + 24
= 56 + 24
= $80
Answer(s): $80
