Barbara has some sweets and caramel apples. If she packs a sweet and a caramel apple in each bag, there will be 10 caramel apples left. If she packs 2 sweets and 3 caramel apples in each bag, there will be 19 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 + 10 |
2 p + 19 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
10 |
19 |
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 = 2 p + 19 --- (1)
1 u + 10 = 3 p
1 u = 3 p - 10 --- (2)
(2) = (1)
3 p - 10 = 2 p + 19
3 p - 2 p = 19 + 10
1 p = 29
Total number of sweets and caramel apples
= (2 p + 19) + 3 p
= 5 p + 19
= 5 x 29 + 19
= 145 + 19
= 164
Answer(s): 164
