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555-605 (Medium)|   Algebra|      
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vikasp99
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Larry’s Lawn Service charges $w/hour for the first x hours of grass tr 02 Mar 2017, 20:01
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

77% (02:55) correct 23% (02:36) wrong based on 108 sessions

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Larry’s Lawn Service charges $w/hour for the first x hours of grass trimming, then w + 2 dollars for every hour of work over x hours. How much more will a homeowner be charged for a grass trimming job that took z hours if z > x than for a job which took only w hours if x < w < z?

A. x(z + w)

B. (w + 2) – zx

C. (w + 2) (z – w)

D. (xw + 2) – (z – w)

E. w(x + z) + x
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C
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KarishmaB
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Larry’s Lawn Service charges $w/hour for the first x hours of grass tr 02 Mar 2017, 23:12
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vikasp99
Larry’s Lawn Service charges $w/hour for the first x hours of grass trimming, then w + 2 dollars for every hour of work over x hours. How much more will a homeowner be charged for a grass trimming job that took z hours if z > x than for a job which took only w hours if x < w < z?

A. x(z + w)

B. (w + 2) – zx

C. (w + 2) (z – w)

D. (xw + 2) – (z – w)

E. w(x + z) + x
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Assume some values. Since x < w < z, assume x = 1, w = 2 and z = 3.

So the charge is $2 per hour for the first 1 hr. Thereafter, it is $4 per hour.
Charge for z (= 3) hrs = 2 + 4 + 4 = $10
Charge for w (= 2 ) hrs = 2 + 4 = $6

A homeowner will be charged $10 - $6 = $4 extra.
The option that gives us $4 will be the answer.

Answer (C)
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Larry’s Lawn Service charges $w/hour for the first x hours of grass tr 02 Mar 2017, 23:46
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vikasp99
Larry’s Lawn Service charges $w/hour for the first x hours of grass trimming, then w + 2 dollars for every hour of work over x hours. How much more will a homeowner be charged for a grass trimming job that took z hours if z > x than for a job which took only w hours if x < w < z?

A. x(z + w)

B. (w + 2) – zx

C. (w + 2) (z – w)

D. (xw + 2) – (z – w)

E. w(x + z) + x
Show more

charge for grass trimming that took w hours = x + w(w+2) ( since x<w )
charge for grass trimming that took z hours = x + z(w+2) ( since x<z )

homeowner will be charged for a grass trimming job that took z hours if z > x than for a job which took only w hours if x < w < z
= x + z(w+2) - x - w(w+2)
= z(w+2) - w(w+2)
= (w+2) (z-w)

Hence option C is correct
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vmelgargalan
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Larry’s Lawn Service charges $w/hour for the first x hours of grass tr 24 Mar 2017, 07:50
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vikasp99
Larry’s Lawn Service charges $w/hour for the first x hours of grass trimming, then w + 2 dollars for every hour of work over x hours. How much more will a homeowner be charged for a grass trimming job that took z hours if z > x than for a job which took only w hours if x < w < z?

A. x(z + w)

B. (w + 2) – zx

C. (w + 2) (z – w)

D. (xw + 2) – (z – w)

E. w(x + z) + x

charge for grass trimming that took w hours = x + w(w+2) ( since x<w )
charge for grass trimming that took z hours = x + z(w+2) ( since x<z )

homeowner will be charged for a grass trimming job that took z hours if z > x than for a job which took only w hours if x < w < z
= x + z(w+2) - x - w(w+2)
= z(w+2) - w(w+2)
= (w+2) (z-w)

Hence option C is correct
Hit Kudos if you liked it 8-)
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charge for grass trimming that took w hours = x + w(w+2) ( since x<w )
charge for grass trimming that took z hours = x + z(w+2) ( since x<z )

I am confused as to why you use x + w(w+2) instead of xw + w(w+2) ; since you are working x hours at w rate
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Larry’s Lawn Service charges $w/hour for the first x hours of grass tr 16 Mar 2021, 06:02
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