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 + 21 1/5 =
h =
hours
To find the number of hours Richard needs to work to reach a total of 30 hours for the week, we can set up the equation:
h + 21 1/5 = 30
To solve the equation, we need to isolate the variable h on one side of the equation.
Subtract 21 1/5 from both sides of the equation:
h = 30 - 21 1/5
To subtract 21 1/5 from 30, we need to find a common denominator for the fractions.
The common denominator for 1/5 is 5.
30 - 21 1/5 can be rewritten as:
30 - (21 + 1/5)
Now, combine the whole numbers:
30 - 21 = 9
Combine the fractions:
1/5
Therefore, the equation becomes:
h = 9 - 1/5
Subtract 1/5 from 9:
h = 8 4/5
So, Richard needs to work 8 hours and 4/5 of an hour 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 set up and solve an equation.
We have already established that Richard worked for 21 1/5 hours in the first three days of the week. To find the remaining hours, h, we need to subtract this from the total target hours of 30.
The equation is as follows:
h + 21 1/5 = 30
To solve this equation, we need to isolate h on one side of the equation by subtracting 21 1/5 from both sides:
h + 21 1/5 - 21 1/5 = 30 - 21 1/5
Simplifying the left side:
h + 0 = 30 - 21 1/5
h = 30 - 21 1/5
To subtract the mixed numbers, we need to convert them to improper fractions:
h = 30 - 21 1/5
h = 30 - (20/1 + 1/5)
h = 30 - (100/5 + 1/5)
h = 30 - (101/5)
Next, we need to find a common denominator and combine the fractions:
h = 30 - (101/5)
h = 30 - (101/5)
h = (150/5) - (101/5)
h = (150 - 101)/5
h = 49/5
Therefore, the number of hours Richard needs to work to reach 30 hours for the week is 49/5 hours, which is equivalent to 9 and 4/5 hours.
h + 21 1/5 = 30
To solve for h, we need to isolate it on one side of the equation.
Subtract 21 1/5 from both sides:
h = 30 - 21 1/5
To subtract the mixed numbers, we need to convert 30 to a mixed number with the same denominator as 1/5.
30 = 29 + 1= 29 5/5 + 1/5 = 29 1/5
The equation becomes:
h = 29 1/5 - 21 1/5
Subtract the whole numbers:
h = 8 1/5
Therefore, Richard needs to work 8 1/5 hours to reach a total of 30 hours for the week.