Xylia has some candy canes and mini cupcakes. If she packs a candy cane and a mini cupcake in each bag, there will be 10 mini cupcakes left. If she packs 3 candy canes and 4 mini cupcakes in each bag, there will be 13 candy canes left. How many candy canes and mini cupcakes does she have in all?
| |
Case 1 |
Case 2 |
| |
Candy Canes |
Mini Cupcakes |
Candy Canes |
Mini Cupcakes |
| Before |
1 u |
1 u + 10 |
3 p + 13 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
10 |
13 |
0 |
The number of candy canes at first is the same for Case 1 and 2.
The number of mini cupcakes at first is also the same for Case 1 and 2.
1 u = 3 p + 13 --- (1)
1 u + 10 = 4 p
1 u = 4 p - 10 --- (2)
(2) = (1)
4 p - 10 = 3 p + 13
4 p - 3 p = 13 + 10
1 p = 23
Total number of candy canes and mini cupcakes
= (3 p + 13) + 4 p
= 7 p + 13
= 7 x 23 + 13
= 161 + 13
= 174
Answer(s): 174
