High School

What is the missing numerator?

\[\frac{\text{blank}}{5} + \frac{18}{20} = \frac{30}{20}\]

A. 8

B. 5

C. 3

D. 2

Answer :

Given:

[tex]\dfrac{?}{5}+\dfrac{18}{20}=\dfrac{30}{20}[/tex]

To find:

The missing value.

Solution:

Let x be the missing value.

We have,

[tex]\dfrac{x}{5}+\dfrac{18}{20}=\dfrac{30}{20}[/tex]

[tex]\dfrac{x}{5}+\dfrac{9}{10}=\dfrac{3}{2}[/tex]

Subtract [tex]\dfrac{9}{10}[/tex] from both sides.

[tex]\dfrac{x}{5}=\dfrac{3}{2}-\dfrac{9}{10}[/tex]

[tex]\dfrac{x}{5}=\dfrac{15-9}{10}[/tex]

[tex]\dfrac{x}{5}=\dfrac{6}{10}[/tex]

[tex]\dfrac{x}{5}=\dfrac{3}{5}[/tex]

Multiplying both sides by 5, we get

[tex]x=3[/tex]

So, the missing value is 3.

Therefore, the correct option is C.