Zara has some caramel apples and chocolate bars. If she packs a caramel apple and a chocolate bar in each bag, there will be 20 chocolate bars left. If she packs 2 caramel apples and 3 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 + 20 |
2 p + 30 |
3 p |
Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
After |
0 |
20 |
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 = 2 p + 30 --- (1)
1 u + 20 = 3 p
1 u = 3 p - 20 --- (2)
(2) = (1)
3 p - 20 = 2 p + 30
3 p - 2 p = 30 + 20
1 p = 50
Total number of caramel apples and chocolate bars
= (2 p + 30) + 3 p
= 5 p + 30
= 5 x 50 + 30
= 250 + 30
= 280
Answer(s): 280