Question

If a fraction is equal to 3/7 and the sum of the numerator and denominator is 100, what is the fraction?

Answer 1

The fraction is equal to 3/7

the sum of numerator and denominator is equal to 100

Let the numerator = x

Since, Numerator + Denominator = 100

x + Denominator = 100

Denominator = 100 - x

Thus, the fraction is in the form of;

`(Numerator)/(Deno\min ator)=(x)/(100-x)`

Since it is given that the fraction is equal to 3/7

So,

`(x)/(100-x)=(3)/(7)`

Simplify the expression for x;

`\begin{gathered} (x)/(100-x)=(3)/(7) \\ \text{ Apply crossmultiplication;} \\ 7x=3(100-x) \\ 7x=300-3x \\ 7x+3x=300 \\ 10x=300 \\ x=(300)/(10) \\ x=30 \end{gathered}`

So, the numerator is 30

Since, Denominator = 100 - x

Substitute x = 30

Denominator = 100 - x

Denominator = 100 - 30

Denominator = 70

Thus, we have numerato = 30 denominator = 70

So, the resulting fraction is given as;

`(30)/(70)`

Answer: 30/70