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A manufacturer produces a certain men's athletic shoe in

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A manufacturer produces a certain men's athletic shoe in [#permalink] New post 13 Feb 2013, 16:42
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A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 20% longer than the smallest size, how long, in inches, is the shoe in size 15?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!
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Re: A manufacturer produces a certain men's athletic shoes... [#permalink] New post 13 Feb 2013, 17:08
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KAS1 wrote:
A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 20% longer than the smallest size, how long, in inches, is the shoe in size 15?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

8 - k inches
9 - k + 0.25 inches

17 = ?

17 = k + 9 * 0.25 = K + 2.25

k + 2.25 = 1.2k

k = 2.25/0.2 = 11.25

Size of 15 = k + 7 * 0.25

= 11.25 + 1.75 = 13

Answer - E
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Re: A manufacturer produces a certain men's athletic shoes... [#permalink] New post 13 Feb 2013, 17:32
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Re: A manufacturer produces a certain men's athletic shoes... [#permalink] New post 13 Feb 2013, 20:07
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KAS1 wrote:
A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 20% longer than the smallest size, how long, in inches, is the shoe in size 15?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!


From size 8 to size 17, there are 9 increments of .25 each making the size 17 shoe 9*.25 = 2.25 inches more than the size 8 shoe.
This 2.25 accounts for 20% of the length of size 8 shoe so length of size 8 shoe is 2.25*5 = 11.25 inches
Length of size 15 shoe must be 11.25 + .25*7 = 13 inches
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Re: A manufacturer produces a certain men's athletic shoes... [#permalink] New post 14 Feb 2013, 01:55
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Let the length of the smallest shoe size(8) be x. Thus the length for size 17 is 1.2x. Now, we know that

x+9*(1/4) =1.2x

Thus, 0.2x = 9/4.

Multiply on both sides by 6,

1.2x = 9*6/4. Thus the length of size 15 shoe is : 1.2x-2*(1/4) = 9*6/4 - 1/2 = 26/2 = 13.

E.
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Re: A manufacturer produces a certain men's athletic shoe in [#permalink] New post 14 Feb 2013, 07:02
Thank you so much! Now this problem makes sense.
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Re: A manufacturer produces a certain men's athletic shoe in [#permalink] New post 14 Feb 2013, 07:44
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8-----9-----10-----11-----12-----13-----14-------15-------16--------17
x----------------------------x+1-------------------x+1.75----x+2------x+2.25

Condition 17 is 20% greater than 8 --------> x+2.25 = x+(20/100)x --------->100x + 225 = 120x --------> x=11.25 --------> x+1.75 = 13 simple enough
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Re: A manufacturer produces a certain men's athletic shoe in   [#permalink] 14 Feb 2013, 07:44
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