Eva has some lollipops and caramel apples. If she packs a lollipop and a caramel apple in each bag, there will be 21 caramel apples left. If she packs 3 lollipops and 4 caramel apples in each bag, there will be 15 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 + 21 |
3 p + 15 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
21 |
15 |
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 + 15 --- (1)
1 u + 21 = 4 p
1 u = 4 p - 21 --- (2)
(2) = (1)
4 p - 21 = 3 p + 15
4 p - 3 p = 15 + 21
1 p = 36
Total number of lollipops and caramel apples
= (3 p + 15) + 4 p
= 7 p + 15
= 7 x 36 + 15
= 252 + 15
= 267
Answer(s): 267
