Answer:
60 Hours
Step-by-step explanation:
First let's get all fractions equivalent.
1/5 7/12 1/20 We can make the common denominator 60
12/60 35/60 3/60
So these three parts of his week take up 50/60 or 5/6 of his time. That means he only has 1/6 left. The question also tells us after all of this he only has 10 hours left, so 1/6 = 10 hours. If you have 1/6 of something how do you find one whole? or 6/6. You multiply it by 6. so 10*6 = 60, which means every week he works 60 hours.
Keith works for 60 hours in a week.
Let the number of working hours for Keith in a week = 'x'
Statement given in the question,
"Keith spends one-fifth of his time in planning and buying merchandise"
Expression for the time spent = [tex]\frac{1}{5}x[/tex] hours
"He spends seven-twelfths of his time in customer service and one-twentieth of his time training the staff"
As per statement expression for the time spent = [tex](\frac{7}{12}x+ \frac{1}{20}x)[/tex] hours
Total time spent by Keith = [tex]\frac{1}{5}x+\frac{7}{12}x+\frac{1}{20}x[/tex]
Expression for the time remaining = [tex]x-(\frac{1}{5}x+\frac{7}{12}x+\frac{1}{20}x)[/tex]
If the time remaining with Keith = 10 hours
Expression for the time remaining hours will become,
[tex]x-(\frac{1}{5}x+\frac{7}{12}x+\frac{1}{20}x)=10[/tex]
Simplify the equation,
[tex]x-x(\frac{12+35+3}{60} )=10[/tex]
[tex]x-x(\frac{50}{60})=10[/tex]
[tex]x-\frac{5}{6}x=10[/tex]
[tex]\frac{6x-5x}{6}=10[/tex]
[tex]x=60[/tex]
Therefore, Keith works for 60 hours each week.
Learn more about the algebraic expression for the statement here,
https://brainly.com/question/24865255?referrer=searchResults
