Rachel and Gem have some money. If Rachel spends $34, she will have
25 as much money as Gem. If Gem spends $6, Rachel will have
56 as much money as Gem. How much money does Rachel have?
| |
Case 1 |
Case 2 |
| |
Rachel |
Gem |
Rachel |
Gem |
| Before |
2 u + $34 |
5 u |
5 p |
6 p + $6 |
| Change |
- $34 |
|
|
- $6 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Rachel has at first in Case 1 and Case 2 is the same.
2 u + 34 = 5 p
2 u = 5 p - 34 --- (1)
The amount that Gem has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 6 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 170 --- (3)
(2)
x 210 u = 12 p + 12 --- (4)
(3) = (4)
25 p - 170 = 12 p + 12
25 p - 12 p = 170 + 12
13 p = 182
1 p = 182 ÷ 13 = 14
Amount that Rachel has
= 5 p
= 5 x 14
= $70
Answer(s): $70
