Lucy has some caramel apples and sweets. If she packs a caramel apple and a sweet in each bag, there will be 16 sweets left. If she packs 5 caramel apples and 6 sweets in each bag, there will be 17 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 + 16 |
5 p + 17 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
16 |
17 |
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 + 17 --- (1)
1 u + 16 = 6 p
1 u = 6 p - 16 --- (2)
(2) = (1)
6 p - 16 = 5 p + 17
6 p - 5 p = 17 + 16
1 p = 33
Total number of caramel apples and sweets
= (5 p + 17) + 6 p
= 11 p + 17
= 11 x 33 + 17
= 363 + 17
= 380
Answer(s): 380
