Shannon and Barbara have some money. If Shannon spends $23, she will have
25 as much money as Barbara. If Barbara spends $1, Shannon will have
56 as much money as Barbara. How much money does Barbara have?
| |
Case 1 |
Case 2 |
| |
Shannon |
Barbara |
Shannon |
Barbara |
| Before |
2 u + $23 |
5 u |
5 p |
6 p + $1 |
| Change |
- $23 |
|
|
- $1 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Shannon has at first in Case 1 and Case 2 is the same.
2 u + 23 = 5 p
2 u = 5 p - 23 --- (1)
The amount that Barbara 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 - 115 --- (3)
(2)
x 210 u = 12 p + 2 --- (4)
(3) = (4)
25 p - 115 = 12 p + 2
25 p - 12 p = 115 + 2
13 p = 117
1 p = 117 ÷ 13 = 9
Amount that Barbara has
= 6 p + 1
= 6 x 9 + 1
= 54 + 1
= $55
Answer(s): $55
