Tammy has some chocolate bars and lollipops. If she packs a chocolate bar and a lollipop in each bag, there will be 16 lollipops left. If she packs 3 chocolate bars and 4 lollipops in each bag, there will be 13 chocolate bars left. How many chocolate bars and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Chocolate Bars |
Lollipops |
Chocolate Bars |
Lollipops |
| Before |
1 u |
1 u + 16 |
3 p + 13 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
16 |
13 |
0 |
The number of chocolate bars 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 = 3 p + 13 --- (1)
1 u + 16 = 4 p
1 u = 4 p - 16 --- (2)
(2) = (1)
4 p - 16 = 3 p + 13
4 p - 3 p = 13 + 16
1 p = 29
Total number of chocolate bars and lollipops
= (3 p + 13) + 4 p
= 7 p + 13
= 7 x 29 + 13
= 203 + 13
= 216
Answer(s): 216
