Kathy has some caramel apples and sweets. If she packs a caramel apple and a sweet in each bag, there will be 29 sweets left. If she packs 5 caramel apples and 6 sweets in each bag, there will be 15 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 + 29 |
5 p + 15 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
29 |
15 |
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 + 15 --- (1)
1 u + 29 = 6 p
1 u = 6 p - 29 --- (2)
(2) = (1)
6 p - 29 = 5 p + 15
6 p - 5 p = 15 + 29
1 p = 44
Total number of caramel apples and sweets
= (5 p + 15) + 6 p
= 11 p + 15
= 11 x 44 + 15
= 484 + 15
= 499
Answer(s): 499
