Jaslyn has some mochi balls and sweets. If she packs a mochi ball and a sweet in each bag, there will be 14 sweets left. If she packs 3 mochi balls and 4 sweets in each bag, there will be 25 mochi balls left. How many mochi balls and sweets does she have in all?
| |
Case 1 |
Case 2 |
| |
Mochi Balls |
Sweets |
Mochi Balls |
Sweets |
| Before |
1 u |
1 u + 14 |
3 p + 25 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
14 |
25 |
0 |
The number of mochi balls at first is the same for Case 1 and 2.
The number of sweets at first is also the same for Case 1 and 2.
1 u = 3 p + 25 --- (1)
1 u + 14 = 4 p
1 u = 4 p - 14 --- (2)
(2) = (1)
4 p - 14 = 3 p + 25
4 p - 3 p = 25 + 14
1 p = 39
Total number of mochi balls and sweets
= (3 p + 25) + 4 p
= 7 p + 25
= 7 x 39 + 25
= 273 + 25
= 298
Answer(s): 298
