Mary has some caramel apples and chocolate bars. If she packs a caramel apple and a chocolate bar in each bag, there will be 23 chocolate bars left. If she packs 3 caramel apples and 4 chocolate bars in each bag, there will be 30 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 + 23 |
3 p + 30 |
4 p |
Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
After |
0 |
23 |
30 |
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 = 3 p + 30 --- (1)
1 u + 23 = 4 p
1 u = 4 p - 23 --- (2)
(2) = (1)
4 p - 23 = 3 p + 30
4 p - 3 p = 30 + 23
1 p = 53
Total number of caramel apples and chocolate bars
= (3 p + 30) + 4 p
= 7 p + 30
= 7 x 53 + 30
= 371 + 30
= 401
Answer(s): 401