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pantera1 [17]
3 years ago
7

A 7 foot piece of PVC pipe is cut into three pieces. The longest piece is 13 inches longer than three times the smallest piece.

The middle piece is 5 inches less than the longest piece. How long is the middle piece? Round your answers to the nearest inch, if necessary.
Mathematics
1 answer:
ohaa [14]3 years ago
8 0

Let x represent length of smallest piece.

We have been given that the longest piece is 13 inches longer than three times the smallest piece. So length of longest piece would be 3x+13.

The middle piece is 5 inches less than the longest piece. So length of middle piece would be 3x+13-5=3x+8.

We have been given that the length of pipe is 7 foot.

1 feet = 12 inches.

7 feet = 7*12 inches = 84 inches.

Now we will equate the sum of lengths of 3 pipes with 84 as:

x+3x+13+3x+8=84

Let us solve for x.

7x+21=84

7x+21-21=84-21

7x=63

\frac{7x}{7}=\frac{63}{7}

x=9

Length of middle piece would be 3x+8\Rightarrow 3(9)+8=27+8=35.

Therefore, the middle piece is 35 inches long.

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First, let's put the second equation, <span>x-2.23y+10.34=0, in terms of y:
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Now we can substitute the right side of this equation for y in the first equation
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Turn it into a quadratic by getting 0 on one side:
2x^2 + 8x - .45x - 4.64 = 0
2x^2 + 7.55x - 4.64 = 0 Divide both sides by 2
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Plug the x values into y = .45x + 4.64
y = .45 (.54) + 4.64
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y = .45 (-4.31) + 4.64
y = 2.70 when x= -4.31

Solution set:
{ (0.54, 4.88) , (-4.31, 2.70) }
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