Xuan has some mini cupcakes and caramel apples. If she packs a mini cupcake and a caramel apple in each bag, there will be 18 caramel apples left. If she packs 4 mini cupcakes and 5 caramel apples in each bag, there will be 29 mini cupcakes left. How many mini cupcakes and caramel apples does she have in all?
|
Case 1 |
Case 2 |
|
Mini Cupcakes |
Caramel Apples |
Mini Cupcakes |
Caramel Apples |
Before |
1 u |
1 u + 18 |
4 p + 29 |
5 p |
Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
After |
0 |
18 |
29 |
0 |
The number of mini cupcakes at first is the same for Case 1 and 2.
The number of caramel apples at first is also the same for Case 1 and 2.
1 u = 4 p + 29 --- (1)
1 u + 18 = 5 p
1 u = 5 p - 18 --- (2)
(2) = (1)
5 p - 18 = 4 p + 29
5 p - 4 p = 29 + 18
1 p = 47
Total number of mini cupcakes and caramel apples
= (4 p + 29) + 5 p
= 9 p + 29
= 9 x 47 + 29
= 423 + 29
= 452
Answer(s): 452