Eva has some caramel apples and sweets. If she packs a caramel apple and a sweet in each bag, there will be 22 sweets left. If she packs 5 caramel apples and 6 sweets in each bag, there will be 16 caramel apples left. How many caramel apples and sweets does she have in all?
|
Case 1 |
Case 2 |
|
Caramel Apples |
Sweets |
Caramel Apples |
Sweets |
Before |
1 u |
1 u + 22 |
5 p + 16 |
6 p |
Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
After |
0 |
22 |
16 |
0 |
The number of caramel apples at first is the same for Case 1 and 2.
The number of sweets at first is also the same for Case 1 and 2.
1 u = 5 p + 16 --- (1)
1 u + 22 = 6 p
1 u = 6 p - 22 --- (2)
(2) = (1)
6 p - 22 = 5 p + 16
6 p - 5 p = 16 + 22
1 p = 38
Total number of caramel apples and sweets
= (5 p + 16) + 6 p
= 11 p + 16
= 11 x 38 + 16
= 418 + 16
= 434
Answer(s): 434