Abi and Xandra have some money. If Abi spends $13, she will have
25 as much money as Xandra. If Xandra spends $17, Abi will have
57 as much money as Xandra. How much money does Abi have?
| |
Case 1 |
Case 2 |
| |
Abi |
Xandra |
Abi |
Xandra |
| Before |
2 u + $13 |
5 u |
5 p |
7 p + $17 |
| Change |
- $13 |
|
|
- $17 |
| After |
2 u |
5 u |
5 p |
7 p |
The amount that Abi has at first in Case 1 and Case 2 is the same.
2 u + 13 = 5 p
2 u = 5 p - 13 --- (1)
The amount that Xandra has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 17 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 65 --- (3)
(2)
x 210 u = 14 p + 34 --- (4)
(3) = (4)
25 p - 65 = 14 p + 34
25 p - 14 p = 65 + 34
11 p = 99
1 p = 99 ÷ 11 = 9
Amount that Abi has
= 5 p
= 5 x 9
= $45
Answer(s): $45
