Hilda has some sweets and mochi balls. If she packs a sweet and a mochi ball in each bag, there will be 29 mochi balls left. If she packs 3 sweets and 4 mochi balls in each bag, there will be 20 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 + 29 |
3 p + 20 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
29 |
20 |
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 = 3 p + 20 --- (1)
1 u + 29 = 4 p
1 u = 4 p - 29 --- (2)
(2) = (1)
4 p - 29 = 3 p + 20
4 p - 3 p = 20 + 29
1 p = 49
Total number of sweets and mochi balls
= (3 p + 20) + 4 p
= 7 p + 20
= 7 x 49 + 20
= 343 + 20
= 363
Answer(s): 363
