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An interior designer decides to accent a wall with an evenly

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An interior designer decides to accent a wall with an evenly [#permalink] New post   24 Nov 2020, 08:28
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An interior designer decides to accent a wall with an evenly spaced row of stenciled circles. The wall is 31 feet 6 inches long, and each stenciled circle has an area of 36π square inches. If the designer wants to leave a space of x inches between each circle and at either end of the row, with no space left over, and x must be an integer, then what is the greatest possible number of circles that the designer can use?

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Re: An interior designer decides to accent a wall with an evenly [#permalink] New post   24 Dec 2020, 04:46
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Length of wall = 31*12 + 6 =378......(1 feet =12 inches)
Area of circle = pi*(radius^2) = 36 pi
radius = 6
diameter=12
x is the space in between circles. To maximize the number of circles, we need to minimize the space in between the circles.
Also, as per the question, x is an integer.
Therefore, least integer we can consider is 1.
Now let p be the number of circles.
If there are x circles there will be x+1 spaces in between.
Now, length of wall = No. of circle*Length of diameter + Number of spaces * Length of each space
So, 12p+(p+1)(1)=378
Thus, 13p=377
p=29
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Re: An interior designer decides to accent a wall with an evenly [#permalink] New post   25 Nov 2020, 01:03
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An interior designer decides to accent a wall with an evenly [#permalink] New post   08 Oct 2021, 19:47
freespirit113 wrote:
Length of wall = 31*12 + 6 =378......(1 feet =12 inches)
Area of circle = pi*(radius^2) = 36 pi
radius = 6
diameter=12
x is the space in between circles. To maximize the number of circles, we need to minimize the space in between the circles.
Also, as per the question, x is an integer.
Therefore, least integer we can consider is 1.
Now let p be the number of circles.
If there are x circles there will be x+1 spaces in between.
Now, length of wall = No. of circle*Length of diameter + Number of spaces * Length of each space
So, 12p+(p+1)(1)=378
Thus, 13p=377
p=29


If the wall starts with a circle and ends with a circle (designer wants to leave a space of x inches between each circle and at either end of the row, with no space left over) then how come the number of circles is smaller than the number of spaces.

For example: O is circle and - is space.

|O-O-O|
|O-O-O-O-O-O|
|O-O-O-O-O-O-O-O-O-O-O-O|

Please explain.
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victiiii
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Re: An interior designer decides to accent a wall with an evenly [#permalink] New post   18 Oct 2021, 01:08
computerbot wrote:
freespirit113 wrote:
Length of wall = 31*12 + 6 =378......(1 feet =12 inches)
Area of circle = pi*(radius^2) = 36 pi
radius = 6
diameter=12
x is the space in between circles. To maximize the number of circles, we need to minimize the space in between the circles.
Also, as per the question, x is an integer.
Therefore, least integer we can consider is 1.
Now let p be the number of circles.
If there are x circles there will be x+1 spaces in between.
Now, length of wall = No. of circle*Length of diameter + Number of spaces * Length of each space
So, 12p+(p+1)(1)=378
Thus, 13p=377
p=29


If the wall starts with a circle and ends with a circle (designer wants to leave a space of x inches between each circle and at either end of the row, with no space left over) then how come the number of circles is smaller than the number of spaces.

For example: O is circle and - is space.

|O-O-O|
|O-O-O-O-O-O|
|O-O-O-O-O-O-O-O-O-O-O-O|

Please explain.



at either end of the row

This suggests that we need to start from a space and end with a space too.
SO the pattern will be:

-O-O-O-O-O-O-
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Re: An interior designer decides to accent a wall with an evenly [#permalink] New post   03 Oct 2024, 03:32
1
Wait your answer is right but the way you guys did is wrong because the question says at either end
so the situation will be one of these two : _circle_circle_circle_circle_circle OR circle_circle_circle_circle_circle_circle_
in any case the number of spaces == number of circles
now let c be the number of circles and we want to minimize the space so let it be 1 and the diameter of a circle is 12 as given in the equation.
so the real equation will be 12c +1c = 378(length in inches)
13c = 378
c = 29.07
so we can only make 29 full circles that is the right answer
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Re: An interior designer decides to accent a wall with an evenly [#permalink]
03 Oct 2024, 03:32
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