Risa has some lollipops and mochi balls. If she packs a lollipop and a mochi ball in each bag, there will be 13 mochi balls left. If she packs 4 lollipops and 5 mochi balls in each bag, there will be 11 lollipops left. How many lollipops and mochi balls does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Mochi Balls |
Lollipops |
Mochi Balls |
| Before |
1 u |
1 u + 13 |
4 p + 11 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
13 |
11 |
0 |
The number of lollipops 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 + 11 --- (1)
1 u + 13 = 5 p
1 u = 5 p - 13 --- (2)
(2) = (1)
5 p - 13 = 4 p + 11
5 p - 4 p = 11 + 13
1 p = 24
Total number of lollipops and mochi balls
= (4 p + 11) + 5 p
= 9 p + 11
= 9 x 24 + 11
= 216 + 11
= 227
Answer(s): 227
