Nora has some chocolate bars and sweets. If she packs a chocolate bar and a sweet in each bag, there will be 28 sweets left. If she packs 5 chocolate bars and 6 sweets in each bag, there will be 12 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 + 28 |
5 p + 12 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
28 |
12 |
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 + 12 --- (1)
1 u + 28 = 6 p
1 u = 6 p - 28 --- (2)
(2) = (1)
6 p - 28 = 5 p + 12
6 p - 5 p = 12 + 28
1 p = 40
Total number of chocolate bars and sweets
= (5 p + 12) + 6 p
= 11 p + 12
= 11 x 40 + 12
= 440 + 12
= 452
Answer(s): 452
