Shiyun has some sweets and caramel apples. If she packs a sweet and a caramel apple in each bag, there will be 27 caramel apples left. If she packs 4 sweets and 5 caramel apples in each bag, there will be 14 sweets left. How many sweets and caramel apples does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Caramel Apples |
Sweets |
Caramel Apples |
| Before |
1 u |
1 u + 27 |
4 p + 14 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
27 |
14 |
0 |
The number of sweets at first is the same for Case 1 and 2.
The number of caramel apples at first is also the same for Case 1 and 2.
1 u = 4 p + 14 --- (1)
1 u + 27 = 5 p
1 u = 5 p - 27 --- (2)
(2) = (1)
5 p - 27 = 4 p + 14
5 p - 4 p = 14 + 27
1 p = 41
Total number of sweets and caramel apples
= (4 p + 14) + 5 p
= 9 p + 14
= 9 x 41 + 14
= 369 + 14
= 383
Answer(s): 383
