Emma has some lollipops and chocolate bars. If she packs a lollipop and a chocolate bar in each bag, there will be 17 chocolate bars left. If she packs 4 lollipops and 5 chocolate bars in each bag, there will be 27 lollipops left. How many lollipops and chocolate bars does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Chocolate Bars |
Lollipops |
Chocolate Bars |
| Before |
1 u |
1 u + 17 |
4 p + 27 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
17 |
27 |
0 |
The number of lollipops at first is the same for Case 1 and 2.
The number of chocolate bars at first is also the same for Case 1 and 2.
1 u = 4 p + 27 --- (1)
1 u + 17 = 5 p
1 u = 5 p - 17 --- (2)
(2) = (1)
5 p - 17 = 4 p + 27
5 p - 4 p = 27 + 17
1 p = 44
Total number of lollipops and chocolate bars
= (4 p + 27) + 5 p
= 9 p + 27
= 9 x 44 + 27
= 396 + 27
= 423
Answer(s): 423
