Emily has some caramel apples and chocolate bars. If she packs a caramel apple and a chocolate bar in each bag, there will be 21 chocolate bars left. If she packs 5 caramel apples and 6 chocolate bars in each bag, there will be 12 caramel apples left. How many caramel apples and chocolate bars does she have in all?
|
Case 1 |
Case 2 |
|
Caramel Apples |
Chocolate Bars |
Caramel Apples |
Chocolate Bars |
Before |
1 u |
1 u + 21 |
5 p + 12 |
6 p |
Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
After |
0 |
21 |
12 |
0 |
The number of caramel apples at first is the same for Case 1 and 2.
The number of chocolate bars at first is also the same for Case 1 and 2.
1 u = 5 p + 12 --- (1)
1 u + 21 = 6 p
1 u = 6 p - 21 --- (2)
(2) = (1)
6 p - 21 = 5 p + 12
6 p - 5 p = 12 + 21
1 p = 33
Total number of caramel apples and chocolate bars
= (5 p + 12) + 6 p
= 11 p + 12
= 11 x 33 + 12
= 363 + 12
= 375
Answer(s): 375