Ivory has some sweets and lollipops. If she packs a sweet and a lollipop in each bag, there will be 10 lollipops left. If she packs 5 sweets and 6 lollipops in each bag, there will be 22 sweets left. How many sweets and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Lollipops |
Sweets |
Lollipops |
| Before |
1 u |
1 u + 10 |
5 p + 22 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
10 |
22 |
0 |
The number of sweets 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 = 5 p + 22 --- (1)
1 u + 10 = 6 p
1 u = 6 p - 10 --- (2)
(2) = (1)
6 p - 10 = 5 p + 22
6 p - 5 p = 22 + 10
1 p = 32
Total number of sweets and lollipops
= (5 p + 22) + 6 p
= 11 p + 22
= 11 x 32 + 22
= 352 + 22
= 374
Answer(s): 374
