Cindy has some chocolate bars and candy canes. If she packs a chocolate bar and a candy cane in each bag, there will be 24 candy canes left. If she packs 5 chocolate bars and 6 candy canes in each bag, there will be 19 chocolate bars left. How many chocolate bars and candy canes does she have in all?
|
Case 1 |
Case 2 |
|
Chocolate Bars |
Candy Canes |
Chocolate Bars |
Candy Canes |
Before |
1 u |
1 u + 24 |
5 p + 19 |
6 p |
Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
After |
0 |
24 |
19 |
0 |
The number of chocolate bars at first is the same for Case 1 and 2.
The number of candy canes at first is also the same for Case 1 and 2.
1 u = 5 p + 19 --- (1)
1 u + 24 = 6 p
1 u = 6 p - 24 --- (2)
(2) = (1)
6 p - 24 = 5 p + 19
6 p - 5 p = 19 + 24
1 p = 43
Total number of chocolate bars and candy canes
= (5 p + 19) + 6 p
= 11 p + 19
= 11 x 43 + 19
= 473 + 19
= 492
Answer(s): 492