Pamela has some sweets and caramel apples. If she packs a sweet and a caramel apple in each bag, there will be 26 caramel apples left. If she packs 5 sweets and 6 caramel apples in each bag, there will be 25 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 + 26 |
5 p + 25 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
26 |
25 |
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 = 5 p + 25 --- (1)
1 u + 26 = 6 p
1 u = 6 p - 26 --- (2)
(2) = (1)
6 p - 26 = 5 p + 25
6 p - 5 p = 25 + 26
1 p = 51
Total number of sweets and caramel apples
= (5 p + 25) + 6 p
= 11 p + 25
= 11 x 51 + 25
= 561 + 25
= 586
Answer(s): 586
