Question

Solve the linear equation: $0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$.
A) $f = \dfrac{2}{{15}}$
B) $f = \dfrac{9}{4}$
C) $f = \dfrac{2}{7}$
D) $f = \dfrac{3}{5}$

Answer 1

Hint: This is the linear equation with one variable ‘f’. So, we will find the value of variable f. First, convert the decimal number to its equivalent fraction form. Then convert that fraction form to its simplest form. Apply a cross multiplication method and remove brackets. Hence, we will get the value of variable f.

Complete step-by-step solution:
Here, the given linear equation is as below.
$0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$
We can also write the above equation by converting it into fraction form.
Here, there are two numbers after the decimal point. So, we will divide the number by 100.
$ \Rightarrow \dfrac{{25}}{{100}}\left( {4f - 3} \right) = \dfrac{5}{{100}}\left( {10f - 9} \right)$
Let us simplify it to convert the fraction to its simplest form.
$ \Rightarrow \dfrac{1}{4}\left( {4f - 3} \right) = \dfrac{1}{{20}}\left( {10f - 9} \right)$
That is equal to,
$ \Rightarrow \dfrac{{4f - 3}}{4} = \dfrac{{10f - 9}}{{20}}$
Let us apply cross multiplication that is multiply the numerator of the left-hand side by the denominator of the right-hand side and also multiply the numerator of the right-hand side by the denominator of the left-hand side.
$ \Rightarrow 20\left( {4f - 3} \right) = 4\left( {10f - 9} \right)$
By taking 2 as a common factor, we can write the above equation as below.
 $ \Rightarrow 10\left( {4f - 3} \right) = 2\left( {10f - 9} \right)$
Let us multiply to remove brackets.
$ \Rightarrow 40f - 30 = 20f - 18$
Let us solve the above equation.
$ \Rightarrow 40f - 20f = 30 - 18$
Now, apply multiplication.
$ \Rightarrow 20f = 12$
Let us divide 20 into both sides.
$ \Rightarrow f = \dfrac{{12}}{{20}}$
Now, take out 4 as a common factor and cut it to convert the fraction to its simplest form.
$ \Rightarrow f = \dfrac{3}{5}$
Therefore, the final answer is $f = \dfrac{3}{5}$ .

Option D is the correct answer.

Note: To convert the decimal number to a fraction, there are the following steps.
Write down the decimal divided by 1.
Multiply the numerator and the denominator by 10 for every number after the decimal point. (If there are two numbers after the decimal point, then use 100. If there are three decimal numbers after the decimal point, then use 1000.)
Simplify the fraction to its simplest form.