Zara has some chocolate bars and sweets. If she packs a chocolate bar and a sweet in each bag, there will be 14 sweets left. If she packs 3 chocolate bars and 4 sweets in each bag, there will be 23 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 + 14 |
3 p + 23 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
14 |
23 |
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 = 3 p + 23 --- (1)
1 u + 14 = 4 p
1 u = 4 p - 14 --- (2)
(2) = (1)
4 p - 14 = 3 p + 23
4 p - 3 p = 23 + 14
1 p = 37
Total number of chocolate bars and sweets
= (3 p + 23) + 4 p
= 7 p + 23
= 7 x 37 + 23
= 259 + 23
= 282
Answer(s): 282
