At work keith spends one-fifth it his time in planning and buying merchandise. he spends seven-twelfths of his time in customer service and one-twentieth of his time training the staff. this leaves him ten hours to deal with the accounts. how many hours does he work each week?

  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 = 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 = hours

Total time spent by Keith =

Expression for the time remaining =

If the time remaining with Keith = 10 hours

Expression for the time remaining hours will become,

Simplify the equation,

     Therefore, Keith works for 60 hours each week.

Learn more about the algebraic expression for the statement here,

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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.

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