Eva has some lollipops and caramel apples. If she packs a lollipop and a caramel apple in each bag, there will be 22 caramel apples left. If she packs 3 lollipops and 4 caramel apples in each bag, there will be 18 lollipops left. How many lollipops and caramel apples does she have in all?
|
Case 1 |
Case 2 |
|
Lollipops |
Caramel Apples |
Lollipops |
Caramel Apples |
Before |
1 u |
1 u + 22 |
3 p + 18 |
4 p |
Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
After |
0 |
22 |
18 |
0 |
The number of lollipops at first is the same for Case 1 and 2.
The number of caramel apples at first is also the same for Case 1 and 2.
1 u = 3 p + 18 --- (1)
1 u + 22 = 4 p
1 u = 4 p - 22 --- (2)
(2) = (1)
4 p - 22 = 3 p + 18
4 p - 3 p = 18 + 22
1 p = 40
Total number of lollipops and caramel apples
= (3 p + 18) + 4 p
= 7 p + 18
= 7 x 40 + 18
= 280 + 18
= 298
Answer(s): 298