Question

During weekdays, Richard is working as a part-time library assistant at a university. He needs to work for a total of 30 hours a week. For the first three days of the week, he worked 21 1/5
hours. Complete the working equation that represents the number of hours, h
, Richard needs to work to reach 30 hours for the week and solve the equation.(1 point)
h + 21 1/5 =

Answer 1

To represent the total number of hours Richard needs to work for the week, you can set up the equation as follows:

\[
h + 21 \frac{1}{5} = 30
\]

Now, let's convert \(21 \frac{1}{5}\) into an improper fraction:

\[
21 \frac{1}{5} = \frac{21 \times 5 + 1}{5} = \frac{105 + 1}{5} = \frac{106}{5}
\]

Now, we can rewrite the equation:

\[
h + \frac{106}{5} = 30
\]

To isolate \(h\), subtract \(\frac{106}{5}\) from both sides. First, let's convert 30 into a fraction with a denominator of 5:

\[
30 = \frac{30 \times 5}{5} = \frac{150}{5}
\]

Now the equation looks like this:

\[
h + \frac{106}{5} = \frac{150}{5}
\]

Subtract \(\frac{106}{5}\) from both sides:

\[
h = \frac{150}{5} - \frac{106}{5} = \frac{150 - 106}{5} = \frac{44}{5}
\]

Now, convert \(\frac{44}{5}\) back to a mixed number:

\[
\frac{44}{5} = 8 \frac{4}{5}
\]

Thus, Richard needs to work \( \boxed{8 \frac{4}{5}} \) hours to reach his total of 30 hours for the week.