Anna has some mini cupcakes and mochi balls. If she packs a mini cupcake and a mochi ball in each bag, there will be 13 mochi balls left. If she packs 2 mini cupcakes and 3 mochi balls in each bag, there will be 23 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 + 13 |
2 p + 23 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
13 |
23 |
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 = 2 p + 23 --- (1)
1 u + 13 = 3 p
1 u = 3 p - 13 --- (2)
(2) = (1)
3 p - 13 = 2 p + 23
3 p - 2 p = 23 + 13
1 p = 36
Total number of mini cupcakes and mochi balls
= (2 p + 23) + 3 p
= 5 p + 23
= 5 x 36 + 23
= 180 + 23
= 203
Answer(s): 203
