Rachel has some chocolate bars and sweets. If she packs a chocolate bar and a sweet in each bag, there will be 17 sweets left. If she packs 4 chocolate bars and 5 sweets in each bag, there will be 29 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 + 17 |
4 p + 29 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
17 |
29 |
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 = 4 p + 29 --- (1)
1 u + 17 = 5 p
1 u = 5 p - 17 --- (2)
(2) = (1)
5 p - 17 = 4 p + 29
5 p - 4 p = 29 + 17
1 p = 46
Total number of chocolate bars and sweets
= (4 p + 29) + 5 p
= 9 p + 29
= 9 x 46 + 29
= 414 + 29
= 443
Answer(s): 443
