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

Question

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 \( h \) Richard needs to work to reach a total of 30 hours for the week, we can set up the equation as follows:

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

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

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

Now we can rewrite the equation:

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

To isolate \( h \), we will first convert 30 into a fraction with the same denominator of 5:

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

Now substitute this back into the equation:

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

Next, we subtract \( \frac{106}{5} \) from both sides:

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

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

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

Thus, the number of hours \( h \) Richard needs to work is:

\[ h = 8 \frac{4}{5} \text{ hours} \]

So the complete working equation and solution are:

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

\[ h = 8 \frac{4}{5} \text{ hours} \]