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 + 21 1/5 = 30
To solve the equation, we need to subtract 21 1/5 from both sides:
h + 21 1/5 - 21 1/5 = 30 - 21 1/5
This simplifies to:
h = 8 4/5 or 8.8 hours
Thus, Richard needs to work an additional 8.8 hours to reach a total of 30 hours for the week.
To find the number of hours, h, that Richard needs to work to reach 30 hours for the week, we can solve the equation:
h + 21 1/5 = 30
To solve this equation, we first need to convert the mixed number 21 1/5 to an improper fraction.
To convert the whole number 21 to a fraction, we multiply it by the denominator of the fraction (5) and add the numerator (1) to get 21 * 5 + 1 = 106.
So, 21 1/5 is equal to 106/5.
Substituting this value in the equation, we have:
h + 106/5 = 30
To isolate the variable h, we need to remove the fraction. We can do this by multiplying both sides of the equation by the reciprocal of 5, which is 1/5:
(1/5)(h + 106/5) = (1/5)(30)
Simplifying this, we get:
h + 106/25 = 6
Next, we can subtract 106/25 from both sides to isolate h:
h = 6 - 106/25
To subtract these fractions, we need a common denominator, which is 25. So, we convert 6 to a fraction with a denominator of 25:
h = 6/1 - 106/25
Then, we find the common denominator of 25:
h = (6*25)/25 - 106/25
Which simplifies to:
h = 150/25 - 106/25
Finally, subtract the numerators and keep the common denominator:
h = (150 - 106)/25
This simplifies to:
h = 44/25
Therefore, Richard needs to work 44/25 hours to reach a total of 30 hours for the week.
To find the number of hours, h, Richard needs to work to reach 30 hours for the week, we can set up the equation:
h + 21 1/5 = 30
To solve this equation, we need to convert the mixed number 21 1/5 to an improper fraction.
Since 1 whole is equal to 5 fifths, we have:
21 1/5 = 20 + 1/5 = 20 + 1/5
Combining the whole number and the fraction, we have:
21 1/5 = 105/5 + 1/5 = 106/5
Now, we can substitute this value into the equation:
h + 106/5 = 30
To solve for h, we need to isolate it on one side of the equation. We can do this by subtracting 106/5 from both sides:
h + 106/5 - 106/5 = 30 - 106/5
Simplifying, we have:
h = 30 - 106/5
To find a common denominator, we can rewrite 30 as 150/5:
h = 150/5 - 106/5
Subtracting the fractions, we have:
h = (150 - 106)/5
Simplifying further, we find:
h = 44/5
Therefore, Richard needs to work 44/5 hours to reach a total of 30 hours for the week.