100 guests went to a party. there was 100 plates also. each boy has used 2 plates,each girl has used 4 plates and food children used one plate. the number of the girls were more than 16.what is the number of girls? what is the number of boys? and what is the number of children?
Answers
Correcting the question: each girl has used 3 plates.
Assumption:
- Number of boys = x
- Number of girls = y > 16
- Number of children = 100 - x - y
Solution:
For a total number of 100 plates, we can form an equation as follows,
2x + 3y + (100 - x - y)/4 = 100
⇒ 8x + 12y + 100 - x - y = 400
⇒ 7x + 11y = 300
We have found one equation with two variables. We cannot solve it with a direct method. We can consider value of one variable and find the other.
We find a set of solutions:
y x
16 124/7
17 187/7
18 102/7
19 13
20 80/7
21 69/7
22 58/7
23 47/7
24 36/7
25 25/7
26 2
Therefore, (x, y) = (13, 19) & (2, 26).
Answer:
Boys Girls Children
13 19 68
2 26 72
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