Diana and Gem have some money. If Diana spends $24, she will have
25 as much money as Gem. If Gem spends $4, Diana will have
67 as much money as Gem. How much money does Gem have?
| |
Case 1 |
Case 2 |
| |
Diana |
Gem |
Diana |
Gem |
| Before |
2 u + $24 |
5 u |
6 p |
7 p + $4 |
| Change |
- $24 |
|
|
- $4 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Diana has at first in Case 1 and Case 2 is the same.
2 u + 24 = 6 p
2 u = 6 p - 24 --- (1)
The amount that Gem has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 4 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 120 --- (3)
(2)
x 210 u = 14 p + 8 --- (4)
(3) = (4)
30 p - 120 = 14 p + 8
30 p - 14 p = 120 + 8
16 p = 128
1 p = 128 ÷ 16 = 8
Amount that Gem has
= 7 p + 4
= 7 x 8 + 4
= 56 + 4
= $60
Answer(s): $60
