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:

$$44÷5=8\text{(remainder 4)}$$

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: $$h=8\frac{4}{5}\text{ hours}$$