Mary has some sweets and chocolate bars. If she packs a sweet and a chocolate bar in each bag, there will be 18 chocolate bars left. If she packs 5 sweets and 6 chocolate bars in each bag, there will be 18 sweets left. How many sweets and chocolate bars does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Chocolate Bars |
Sweets |
Chocolate Bars |
| Before |
1 u |
1 u + 18 |
5 p + 18 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
18 |
18 |
0 |
The number of sweets at first is the same for Case 1 and 2.
The number of chocolate bars at first is also the same for Case 1 and 2.
1 u = 5 p + 18 --- (1)
1 u + 18 = 6 p
1 u = 6 p - 18 --- (2)
(2) = (1)
6 p - 18 = 5 p + 18
6 p - 5 p = 18 + 18
1 p = 36
Total number of sweets and chocolate bars
= (5 p + 18) + 6 p
= 11 p + 18
= 11 x 36 + 18
= 396 + 18
= 414
Answer(s): 414
