Question

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?

Answer 1

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.

Answer 2

  Keith works for 60 hours in a week.

Algebraic expressions for the statement:

• Assume the variable first.
• Use the statement to convert it into an algebraic expression.

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 = $\frac{1}{5}x$ 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 = $(\frac{7}{12}x+ \frac{1}{20}x)$ hours

Total time spent by Keith = $\frac{1}{5}x+\frac{7}{12}x+\frac{1}{20}x$

Expression for the time remaining = $x-(\frac{1}{5}x+\frac{7}{12}x+\frac{1}{20}x)$

If the time remaining with Keith = 10 hours

Expression for the time remaining hours will become,

$x-(\frac{1}{5}x+\frac{7}{12}x+\frac{1}{20}x)=10$

Simplify the equation,

$x-x(\frac{12+35+3}{60} )=10$

$x-x(\frac{50}{60})=10$

$x-\frac{5}{6}x=10$

$\frac{6x-5x}{6}=10$

$x=60$

     Therefore, Keith works for 60 hours each week.

Learn more about the algebraic expression for the statement here,

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