Questions: What is the solution of the equation 5/12 w + 1/5 = 7/10 ? w = 5/6 w = 25/54 w = 2 4/25 w = 1 1/5

Solution Steps

The given equation is:

\[ \frac{5}{12} w + \frac{1}{5} = \frac{7}{10} \]

First, we need to isolate the term with \( w \). Subtract \(\frac{1}{5}\) from both sides:

\[ \frac{5}{12} w = \frac{7}{10} - \frac{1}{5} \]

To subtract the fractions on the right side, find a common denominator. The least common multiple of 10 and 5 is 10. Convert \(\frac{1}{5}\) to have a denominator of 10:

\[ \frac{1}{5} = \frac{2}{10} \]

Now subtract:

\[ \frac{7}{10} - \frac{2}{10} = \frac{5}{10} = \frac{1}{2} \]

So the equation becomes:

\[ \frac{5}{12} w = \frac{1}{2} \]

To solve for \( w \), multiply both sides by the reciprocal of \(\frac{5}{12}\), which is \(\frac{12}{5}\):

\[ w = \frac{1}{2} \times \frac{12}{5} \]

Calculate the right side:

\[ w = \frac{12}{10} = \frac{6}{5} \]

Final Answer