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 and 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 equation for the number of hours Richard needs to work to reach 30 hours for the week is:
Total hours worked = Target hours - Hours already worked
h = 30 - 21 1/5
To solve this equation, we need to convert the mixed number 21 1/5 to an improper fraction. We can do this by multiplying the whole number (21) by the denominator (5) and adding the numerator (1), then placing the result over the denominator:
21 1/5 = (21 * 5 + 1) / 5 = 106 / 5
Now we can subtract the hours already worked from the target hours:
h = 30 - 106/5
To subtract fractions, we need a common denominator. In this case, the common denominator is 5:
h = (150/5) - (106/5)
Now we can subtract the fractions:
h = 44/5
To simplify the fraction, we can divide the numerator (44) by the denominator (5):
h = 8 4/5
Therefore, Richard needs to work an additional 8 hours and 4/5 of an hour to reach a total of 30 hours for the week.