Question

In Exercises \(32-37\), solve each equation for the unknown quantity. Check your answers. $$\frac{3}{10}=c-\frac{1}{5}$$

Short answer

Question: Given the equation $\frac{3}{10} = c - \frac{1}{5}$, solve for the value of c. Answer: The value of c is $\frac{1}{2}$.

Step-by-step solution

Find the common denominator

In order to add or subtract fractions, we need a common denominator. In this case, we have denominators 10 and 5. The lowest common denominator for these is 10.

Rewrite the fractions with the common denominator

Rewrite the equation with fractions that have a common denominator of 10. $$\frac{3}{10}=c-\frac{1}{5}$$ $$\frac{3}{10}=c-\frac{2}{10}$$

Simplify and isolate the variable

Add the fraction to both sides of the equation to isolate the variable c. $$\frac{3}{10}+\frac{2}{10}=c$$

Solve for c

Add the fractions on the left side. $$\frac{3+2}{10}=c$$ $$\frac{5}{10}=c$$

Simplify the fraction

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD). $$c=\frac{1}{2}$$

Check the solution

Substitute the value of c back into the original equation and see if both sides are equal. $$\frac{3}{10}=\frac{1}{2}-\frac{1}{5}$$ $$\frac{3}{10}=\frac{1\cdot5}{2\cdot5}-\frac{1}{5}$$ $$\frac{3}{10}=\frac{5}{10}-\frac{2}{10}$$ $$\frac{3}{10}=\frac{3}{10}$$ Since the left side equals the right side, we have found the correct solution: $$c=\frac{1}{2}$$