Cathy has some mini cupcakes and chocolate bars. If she packs a mini cupcake and a chocolate bar in each bag, there will be 23 chocolate bars left. If she packs 4 mini cupcakes and 5 chocolate bars in each bag, there will be 26 mini cupcakes left. How many mini cupcakes and chocolate bars does she have in all?
|
Case 1 |
Case 2 |
|
Mini Cupcakes |
Chocolate Bars |
Mini Cupcakes |
Chocolate Bars |
Before |
1 u |
1 u + 23 |
4 p + 26 |
5 p |
Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
After |
0 |
23 |
26 |
0 |
The number of mini cupcakes at first is the same for Case 1 and 2.
The number of chocolate bars at first is also the same for Case 1 and 2.
1 u = 4 p + 26 --- (1)
1 u + 23 = 5 p
1 u = 5 p - 23 --- (2)
(2) = (1)
5 p - 23 = 4 p + 26
5 p - 4 p = 26 + 23
1 p = 49
Total number of mini cupcakes and chocolate bars
= (4 p + 26) + 5 p
= 9 p + 26
= 9 x 49 + 26
= 441 + 26
= 467
Answer(s): 467