MATH PROBLEMS ON CALCULATING NUMBER OF SIBLINGS

If we "b" be the number of boys, then "g" be the number of girls. 

According to each boy's perspective :

He will have (b - 1) brothers and g sisters.

According to each girl's perspective :

She will have (g - 1) sisters and b brothers.

Note :

Here, we subtract 1 from the number of boys to calculate the number of brothers he has. Because each boy will not be a brother of himself.

Like that, we subtract 1 from the number of girls to calculate the number of sisters she has. Because each girl will not be a sister of herself.

Example 1 :

Among the children in a family, each boy has as many sisters as brothers, but each girl has only half as many sisters as brothers. How do you find the number of children in the family?

Solution :

Let "b" and "g" be the number of boys and number of girls respectively in the family.

According to each boy's perspective :

He will have (b - 1) brothers and g sisters.

According to each girl's perspective :

She will have (g - 1) sisters and b brothers.

According to the question, each boy is thinking about his brothers and he says that he has as many sisters as brothers.

We decide that :

Number of sisters  =  Number of brothers he has 

g  =  b - 1  ---------(1)

Now each girl is thinking about her sisters. That is each girl is having only half as many sisters as brothers.

Number of sisters (g - 1)  =  b/2  ---------(2)

From (1),

b  =  g + 1

From (1),

b  =  2(g - 1)

g + 1  =  2(g - 1)

g + 1  =  2g - 2

g - 2g  =  -2 - 1

g  =  3

b  =  3 + 1

b  =  4

So, the number of boys and girls in the family are 4 and 3 respectively.

Hence the number of children in the family is 7.

Example 2 :

In a particular family each boy has as many brothers as sisters but each girl has twice as many brothers as that of sisters. How many siblings are there in the family?

Solution :

Let "b" and "g" be the number of boys and number of girls respectively in the family.

Each boy has "g" sisters and "b - 1" brothers 

Each girl has "b" brothers and "g - 1" sisters

According to each boy's perspective :

Number of brothers he has  =  Number of sisters

b - 1  =  g ----(1)

According to girl's perspective :

b  =  2(g - 1)  ----(2)

From (1),

b  =  g + 1

g + 1  =  2g - 2

g - 2g  =  -2 - 1

-g  =  -3

g  =  3

By applying the value of g, we get the value of b.

b  =  3 + 1

b  =  4

So, the number of boys and girls in the family are 4 and 3 respectively.

Hence the number of children in the family is 7.

Example 3 :

In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in family?

Solution :

Let "b" and "g" be the number of boys and number of girls respectively in the family.

Each boy has "g" sisters and "b - 1" brothers 

Each girl has "b" brothers and "g - 1" sisters

According to girl's  perspective :

g - 1  =  b  ---(1)

According to boy's perspective :

g  =  2(b - 1)  ---(2)

From (1)

g  =  b + 1

By applying the value of g in (2), we get

b + 1  =  2(b - 1)

b + 1  =  2b - 2

b - 2b  =  -2 - 1

-b  =  -3

b  =  3

By applying the value of 

g  =  3 + 1

g  =  4

Hence the family has 3 sons.

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