During weekdays, Richard is working as a part time library assistant at a university. He needs to work off 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
The working equation that represents the number of hours Richard needs to work to reach 30 hours for the week is:
30 - (21 1/5 + h) = 0
To solve the equation, we can start by simplifying the expression inside the parentheses:
21 1/5 + h = 21 1/5 + (5/5)h = (106/5 + 5h/5) = (106 + 5h)/5
Substituting this back into the equation, we have:
30 - (106 + 5h)/5 = 0
To get rid of the fraction, we can multiply both sides of the equation by 5:
5(30) - 106 - 5h = 0
150 - 106 - 5h = 0
44 - 5h = 0
To isolate h, we can subtract 44 from both sides of the equation:
-5h = -44
Finally, we divide both sides by -5:
h = -44 / -5
Simplifying this division, we get:
h = 8.8
So, Richard needs to work approximately 8.8 hours to reach 30 hours for the week.