Usha has some mochi balls and lollipops. If she packs a mochi ball and a lollipop in each bag, there will be 13 lollipops left. If she packs 2 mochi balls and 3 lollipops in each bag, there will be 16 mochi balls left. How many mochi balls and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Mochi Balls |
Lollipops |
Mochi Balls |
Lollipops |
| Before |
1 u |
1 u + 13 |
2 p + 16 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
13 |
16 |
0 |
The number of mochi balls at first is the same for Case 1 and 2.
The number of lollipops at first is also the same for Case 1 and 2.
1 u = 2 p + 16 --- (1)
1 u + 13 = 3 p
1 u = 3 p - 13 --- (2)
(2) = (1)
3 p - 13 = 2 p + 16
3 p - 2 p = 16 + 13
1 p = 29
Total number of mochi balls and lollipops
= (2 p + 16) + 3 p
= 5 p + 16
= 5 x 29 + 16
= 145 + 16
= 161
Answer(s): 161
