Emma has some mini cupcakes and mochi balls. If she packs a mini cupcake and a mochi ball in each bag, there will be 26 mochi balls left. If she packs 5 mini cupcakes and 6 mochi balls in each bag, there will be 18 mini cupcakes left. How many mini cupcakes and mochi balls does she have in all?
| |
Case 1 |
Case 2 |
| |
Mini Cupcakes |
Mochi Balls |
Mini Cupcakes |
Mochi Balls |
| Before |
1 u |
1 u + 26 |
5 p + 18 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
26 |
18 |
0 |
The number of mini cupcakes at first is the same for Case 1 and 2.
The number of mochi balls at first is also the same for Case 1 and 2.
1 u = 5 p + 18 --- (1)
1 u + 26 = 6 p
1 u = 6 p - 26 --- (2)
(2) = (1)
6 p - 26 = 5 p + 18
6 p - 5 p = 18 + 26
1 p = 44
Total number of mini cupcakes and mochi balls
= (5 p + 18) + 6 p
= 11 p + 18
= 11 x 44 + 18
= 484 + 18
= 502
Answer(s): 502
