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.(1 point) h + 2115 = h = hours
The working equation that represents the number of hours Richard needs to work to reach 30 hours for the week is:
h + 21 1/5 = 30
To solve the equation, we need to isolate h by subtracting 21 1/5 from both sides:
h = 30 - 21 1/5
h = 30 - 106/5
h = 150/5 - 106/5
h = 44/5
Therefore, Richard needs to work an additional 44/5 hours, or 8 4/5 hours, to reach a total of 30 hours for the week.
To find the number of hours Richard still needs to work to reach a total of 30 hours for the week, we need to subtract the hours he has already worked from the target of 30 hours.
Given that Richard has already worked 21 1/5 hours, we can convert this mixed number into an improper fraction. 1/5 can be written as 1 divided by 5, which is 1/5 as a fraction.
So, 21 1/5 can be written as (21 * 5 + 1) / 5 = 106/5 hours.
To find the number of hours Richard still needs to work, we subtract the hours he has already worked from the target number of hours:
h = 30 - 106/5
Now, we can simplify the equation by finding a common denominator:
h = (150/5 - 106/5)
Combining the numerators:
h = (150 - 106) / 5
Calculating the difference:
h = 44 / 5
Now, if we convert the improper fraction into a mixed number by dividing the numerator (44) by the denominator (5), we get:
h = 8 remainder 4/5
Therefore, Richard still needs to work 8 and 4/5 hours to reach a total of 30 hours for the week.
To find the number of hours, h, Richard needs to work to reach a total of 30 hours for the week, we can subtract the number of hours he has already worked from 30.
Richard has worked 21 1/5 hours for the first three days of the week. To convert this mixed number to an improper fraction, we multiply the whole number (21) by the denominator (5), and then add the numerator (1). So, 21 1/5 can be written as (21 * 5 + 1)/5 = 106/5.
Now, to find the number of hours Richard still needs to work, we subtract the hours he has already worked from the total number of hours required:
h = 30 - 106/5
To subtract the fraction, we need a common denominator. The common denominator we can use is 5, so:
h = 150/5 - 106/5
Now, we can subtract the fractions:
h = (150 - 106)/5
h = 44/5
Therefore, Richard needs to work 44/5 or 8 4/5 hours to reach a total of 30 hours for the week.
So, the working equation that represents this is:
h + 106/5 = 30
Or, in simplified form:
h + 44/5 = 30
To solve this equation, we can isolate h by subtracting 44/5 from both sides:
h = 30 - 44/5
To subtract the fractions, we need a common denominator:
h = (150/5) - (44/5)
h = 106/5
Therefore, Richard needs to work for a further 106/5 hours or 21 1/5 hours to reach a total of 30 hours for the week.