Question

In a functoin there is total 100 people and 100 cakes. Giving every male has 10 cakes and each female has 5 cakes and a child has half of the cake and how to find the total number of male and female and number of child?

Answer 1

Let the number of male and female be x and y.

Then the number of children are 100 - (x + y).

For a total quantity of 100 cakes:

10x + 5y + {100 - (x + y)}/2 = 100

>> 20x + 10y + 100 - x - y = 200

>> 19x + 9y = 100

>> 19x = 100 - 9y

>> x = (100 - 9y)/19

We have found one equation with two unknown variables. It cannot be solved in a direct method. So we put such values of y for which, we will get a numerator divisible by 19.

Multiples of 19 are 19, 38, 57, 76, 95.

We put values of y and find x:

y x

1 91/19

2 82/19

3 73/19

4 64/19

5 55/19

6 46/19

7 37/19

8 28/19

9 1

10 10/19

11 1/19

Therefore the only possible values are

x = 1, y = 9.

Answer:

Men Women Children

1 9 90

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