Nicole has some caramel apples and chocolate bars. If she packs a caramel apple and a chocolate bar in each bag, there will be 16 chocolate bars left. If she packs 4 caramel apples and 5 chocolate bars in each bag, there will be 18 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 + 16 |
4 p + 18 |
5 p |
Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
After |
0 |
16 |
18 |
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 = 4 p + 18 --- (1)
1 u + 16 = 5 p
1 u = 5 p - 16 --- (2)
(2) = (1)
5 p - 16 = 4 p + 18
5 p - 4 p = 18 + 16
1 p = 34
Total number of caramel apples and chocolate bars
= (4 p + 18) + 5 p
= 9 p + 18
= 9 x 34 + 18
= 306 + 18
= 324
Answer(s): 324