Kathy has some caramel apples and sweets. If she packs a caramel apple and a sweet in each bag, there will be 28 sweets left. If she packs 4 caramel apples and 5 sweets in each bag, there will be 27 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 + 28 |
4 p + 27 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
28 |
27 |
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 = 4 p + 27 --- (1)
1 u + 28 = 5 p
1 u = 5 p - 28 --- (2)
(2) = (1)
5 p - 28 = 4 p + 27
5 p - 4 p = 27 + 28
1 p = 55
Total number of caramel apples and sweets
= (4 p + 27) + 5 p
= 9 p + 27
= 9 x 55 + 27
= 495 + 27
= 522
Answer(s): 522
