Kylie has some caramel apples and lollipops. If she packs a caramel apple and a lollipop in each bag, there will be 29 lollipops left. If she packs 3 caramel apples and 4 lollipops in each bag, there will be 15 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 + 29 |
3 p + 15 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
29 |
15 |
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 = 3 p + 15 --- (1)
1 u + 29 = 4 p
1 u = 4 p - 29 --- (2)
(2) = (1)
4 p - 29 = 3 p + 15
4 p - 3 p = 15 + 29
1 p = 44
Total number of caramel apples and lollipops
= (3 p + 15) + 4 p
= 7 p + 15
= 7 x 44 + 15
= 308 + 15
= 323
Answer(s): 323
