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 =
h = hours

Answer 1

To find the number of hours \( h \) that Richard needs to work to reach a total of 30 hours for the week, we can start with the equation:

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

First, we need to convert \( 21 \frac{1}{5} \) into an improper fraction to make calculations easier:

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

Now, substitute \( 21 \frac{1}{5} \) with \( \frac{106}{5} \) in the equation:

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

Next, 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:

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

To isolate \( h \), subtract \( \frac{106}{5} \) from both sides:

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

Combine the fractions:

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

Now convert \( \frac{44}{5} \) into a mixed number:

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

So, the final answer is:

\[
h + 21 \frac{1}{5} = 30 \\
h = 8 \frac{4}{5} \text{ hours}
\]

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