Wendy has some mochi balls and mini cupcakes. If she packs a mochi ball and a mini cupcake in each bag, there will be 20 mini cupcakes left. If she packs 2 mochi balls and 3 mini cupcakes in each bag, there will be 27 mochi balls left. How many mochi balls and mini cupcakes does she have in all?
| |
Case 1 |
Case 2 |
| |
Mochi Balls |
Mini Cupcakes |
Mochi Balls |
Mini Cupcakes |
| Before |
1 u |
1 u + 20 |
2 p + 27 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
20 |
27 |
0 |
The number of mochi balls 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 = 2 p + 27 --- (1)
1 u + 20 = 3 p
1 u = 3 p - 20 --- (2)
(2) = (1)
3 p - 20 = 2 p + 27
3 p - 2 p = 27 + 20
1 p = 47
Total number of mochi balls and mini cupcakes
= (2 p + 27) + 3 p
= 5 p + 27
= 5 x 47 + 27
= 235 + 27
= 262
Answer(s): 262
