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 \( h \) that 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, let's convert \( 21 \frac{1}{5} \) to an improper fraction for easier calculation.

To convert \( 21 \frac{1}{5} \):

1. Multiply the whole number (21) by the denominator (5): \[ 21 \times 5 = 105 \]
2. Add the numerator (1) to this product: \[ 105 + 1 = 106 \]
3. Place this sum over the denominator (5): \[ 21 \frac{1}{5} = \frac{106}{5} \]

So the equation now looks like this:

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

To solve for \( h \), we can isolate it by subtracting \( \frac{106}{5} \) from both sides:

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

To perform the subtraction, convert 30 to a fraction with a denominator of 5:

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

Now the equation is:

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

Proceed with the subtraction:

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

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

\[ 44 \div 5 = 8 \quad \text{(remainder 4)} \]

This means:

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

Thus, Richard needs to work:

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

Summary:

The complete equation is: \[ h + 21 \frac{1}{5} = 30 \]

And the solution is: \[ h = 8 \frac{4}{5} \text{ hours} \]