Opal has some mochi balls and mini cupcakes. If she packs a mochi ball and a mini cupcake in each bag, there will be 18 mini cupcakes left. If she packs 4 mochi balls and 5 mini cupcakes in each bag, there will be 24 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 + 18 |
4 p + 24 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
18 |
24 |
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 = 4 p + 24 --- (1)
1 u + 18 = 5 p
1 u = 5 p - 18 --- (2)
(2) = (1)
5 p - 18 = 4 p + 24
5 p - 4 p = 24 + 18
1 p = 42
Total number of mochi balls and mini cupcakes
= (4 p + 24) + 5 p
= 9 p + 24
= 9 x 42 + 24
= 378 + 24
= 402
Answer(s): 402
