Betty has some chocolate bars and sweets. If she packs a chocolate bar and a sweet in each bag, there will be 12 sweets left. If she packs 5 chocolate bars and 6 sweets in each bag, there will be 19 chocolate bars left. How many chocolate bars and sweets does she have in all?
|
Case 1 |
Case 2 |
|
Chocolate Bars |
Sweets |
Chocolate Bars |
Sweets |
Before |
1 u |
1 u + 12 |
5 p + 19 |
6 p |
Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
After |
0 |
12 |
19 |
0 |
The number of chocolate bars at first is the same for Case 1 and 2.
The number of sweets at first is also the same for Case 1 and 2.
1 u = 5 p + 19 --- (1)
1 u + 12 = 6 p
1 u = 6 p - 12 --- (2)
(2) = (1)
6 p - 12 = 5 p + 19
6 p - 5 p = 19 + 12
1 p = 31
Total number of chocolate bars and sweets
= (5 p + 19) + 6 p
= 11 p + 19
= 11 x 31 + 19
= 341 + 19
= 360
Answer(s): 360