Yen has some sweets and mochi balls. If she packs a sweet and a mochi ball in each bag, there will be 15 mochi balls left. If she packs 4 sweets and 5 mochi balls in each bag, there will be 13 sweets left. How many sweets and mochi balls does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Mochi Balls |
Sweets |
Mochi Balls |
| Before |
1 u |
1 u + 15 |
4 p + 13 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
15 |
13 |
0 |
The number of sweets 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 = 4 p + 13 --- (1)
1 u + 15 = 5 p
1 u = 5 p - 15 --- (2)
(2) = (1)
5 p - 15 = 4 p + 13
5 p - 4 p = 13 + 15
1 p = 28
Total number of sweets and mochi balls
= (4 p + 13) + 5 p
= 9 p + 13
= 9 x 28 + 13
= 252 + 13
= 265
Answer(s): 265
