Tammy has some caramel apples and lollipops. If she packs a caramel apple and a lollipop in each bag, there will be 24 lollipops left. If she packs 2 caramel apples and 3 lollipops in each bag, there will be 23 caramel apples left. How many caramel apples and lollipops does she have in all?
|
Case 1 |
Case 2 |
|
Caramel Apples |
Lollipops |
Caramel Apples |
Lollipops |
Before |
1 u |
1 u + 24 |
2 p + 23 |
3 p |
Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
After |
0 |
24 |
23 |
0 |
The number of caramel apples 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 = 2 p + 23 --- (1)
1 u + 24 = 3 p
1 u = 3 p - 24 --- (2)
(2) = (1)
3 p - 24 = 2 p + 23
3 p - 2 p = 23 + 24
1 p = 47
Total number of caramel apples and lollipops
= (2 p + 23) + 3 p
= 5 p + 23
= 5 x 47 + 23
= 235 + 23
= 258
Answer(s): 258