Zara has some lollipops and sweets. If she packs a lollipop and a sweet in each bag, there will be 23 sweets left. If she packs 3 lollipops and 4 sweets in each bag, there will be 26 lollipops left. How many lollipops and sweets does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Sweets |
Lollipops |
Sweets |
| Before |
1 u |
1 u + 23 |
3 p + 26 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
23 |
26 |
0 |
The number of lollipops at first is the same for Case 1 and 2.
The number of sweets at first is also the same for Case 1 and 2.
1 u = 3 p + 26 --- (1)
1 u + 23 = 4 p
1 u = 4 p - 23 --- (2)
(2) = (1)
4 p - 23 = 3 p + 26
4 p - 3 p = 26 + 23
1 p = 49
Total number of lollipops and sweets
= (3 p + 26) + 4 p
= 7 p + 26
= 7 x 49 + 26
= 343 + 26
= 369
Answer(s): 369
