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.
To find the number of hours Richard still needs to work, we can subtract the number of hours he has already worked from the total number of hours he needs to work.
Let h be the number of hours Richard still needs to work.
Since Richard has already worked 21 1/5 hours, the equation that represents the number of hours Richard still needs to work is:
h = Total number of hours Richard needs to work - Number of hours Richard has already worked
h = 30 - 21 1/5
To subtract fractions with different denominators, we need to find a common denominator. The common denominator of 5 and 1 is 5.
Converting 30 to fifths: 30 * 5/5 = 150/5
h = 150/5 - 21 1/5
Now, we can subtract the two fractions:
h = (150 - 21)/5
h = 129/5
However, since we are looking for a whole number of hours Richard still needs to work, we need to convert the fraction to a mixed number.
Divide 129 by 5:
129 รท 5 = 25 with a remainder of 4.
This means that Richard still needs to work 25 and 4/5 hours to reach a total of 30 hours for the week.