Fiona has some sweets and caramel apples. If she packs a sweet and a caramel apple in each bag, there will be 12 caramel apples left. If she packs 4 sweets and 5 caramel apples in each bag, there will be 17 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 + 12 |
4 p + 17 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
12 |
17 |
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 + 17 --- (1)
1 u + 12 = 5 p
1 u = 5 p - 12 --- (2)
(2) = (1)
5 p - 12 = 4 p + 17
5 p - 4 p = 17 + 12
1 p = 29
Total number of sweets and caramel apples
= (4 p + 17) + 5 p
= 9 p + 17
= 9 x 29 + 17
= 261 + 17
= 278
Answer(s): 278
