Yoko has some lollipops and sweets. If she packs a lollipop and a sweet in each bag, there will be 30 sweets left. If she packs 5 lollipops and 6 sweets in each bag, there will be 13 lollipops left. How many lollipops and sweets does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Sweets |
Lollipops |
Sweets |
| Before |
1 u |
1 u + 30 |
5 p + 13 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
30 |
13 |
0 |
The number of lollipops 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 = 5 p + 13 --- (1)
1 u + 30 = 6 p
1 u = 6 p - 30 --- (2)
(2) = (1)
6 p - 30 = 5 p + 13
6 p - 5 p = 13 + 30
1 p = 43
Total number of lollipops and sweets
= (5 p + 13) + 6 p
= 11 p + 13
= 11 x 43 + 13
= 473 + 13
= 486
Answer(s): 486
