Sac had a rope that was 15 feet long. He cut it into three pieces. The first piece was 3.57 feet longer than the second piece. The third piece was 2.97 feet longer than the second piece. How long was the third piece of rope?

Answer:

5.79 feet

Step-by-step explanation:

Let us represent

First piece = x

Second piece = y

Third piece = z

Sac had a rope that was 15 feet long.

x + y + z = 15

He cut it into three pieces.

The first piece was 3.57 feet longer than the second piece.

x = 3.57 + y

The third piece was 2.97 feet longer than the second piece.

z = 2.97 + y

How long was the third piece of rope?

x + y + z = 15

3.57 + y + y + 2.97 + y = 15

3y + 6.54 = 15

3y = 15 - 6.54

3y = 8.46

y = 8.46/3

y = 2.82 feet

Therefore, the length of the third piece z = 2.97 + y

z = 2.82 + 2.97

z = 5.79 feet

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[asy]

unitsize(50);

draw(Circle((0,0),1),black+1);

dot((0,0));

for(real i=0;i<360;i+=6){

draw(0.96*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);

};

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draw(0.93*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);

label(string(i/30),0.83*(sin(i*pi/180),cos(i*pi/180)));

};


real h=3.5; real m=30;

draw(0.65*(sin(pi/6*(h)),cos(pi/6*(h)))--(0,0)--0.9*(sin(pi/30*m),cos(pi/30*m)),black+1,Arrows(TeXHead));

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[/asy]

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Negative Direction:

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Positive Direction:

– =

=



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x = –x equals negative StartFraction 29 Over 2 EndFraction or x equals StartFraction 15 Over 2 EndFraction or x =
x = –x equals negative StartFraction 29 Over 2 EndFraction or x equals negative StartFraction 15 Over 2 EndFraction or x = –
x = x equals StartFraction 29 Over 2 EndFraction or x equals StartFraction 15 Over 2 EndFraction or x =

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