Solve the Fraction Equation: Finding the Denominator in 10a/? = 6a/3

Complete the corresponding expression for the denominator

$\frac{10a}{?}=\frac{6a}{3}$

After examining the problem, note that the fraction on the right side can be reduced:

$\frac{10a}{?}=\frac{\not{6}a}{\not{3}} \\ \downarrow\\ \frac{10a}{?}=\frac{2a}{1}$

Using the following factorisation:

$6=2\cdot3$

Remember the process of reducing a fraction:

In both the numerator of the expression on the right side as well as in the numerator of the expression on the left side the expression $a$ is present. Therefore in the expression we are looking for there are no variables (given that we don't want to reduce them from the expression in the numerator on the left side),

Next, we ask which number is placed in the denominator of the expression on the left side so that when reduced with the number 10 it will yield the number 2. The answer to this is of course - the number 5,

Due to the fact that:

$10=2\cdot 5$

Verify that this choice gives us the expression on the right side:

$\frac{10a}{?}=\frac{2a}{1} \\ \downarrow\\ \frac{\not{10}a}{\textcolor{red}{\not{5}}}\stackrel{?}{= }\frac{2a}{1} \\ \downarrow\\ \boxed{\frac{2a}{1}\stackrel{!}{= }\frac{2a}{1}}$

Therefore this choice is indeed correct.

In other words - the correct answer is answer C.