A piece of wire that is 16 meters long is cut into two pieces so that one piece is three fifths as long as the other. Find the length of each piece.

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lemjay | High School Teacher | (Level 3) Senior Educator

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To solve for the length of each of the two pieces, let x be the length of first piece.

Since the second piece is three fifths as long as the first one, then the length of the second piece is 3/5x.

Next, consider the total length of the wire which is 16. So to set-up the equation, add the length of the two pieces and set it equal to 16.

`x+3/5x=16`

Then, simplify the equation by multiplying both sides by the denominator of the fraction.

`5(x+3/5x)=16*5`

`5x+3x=80`

Also, combine like terms.

`8x=80`

And isolate x. So, divide both sides by 8.

`(8x)/8=80/8`

`x=10`

Hence, the length of the first piece is 10 meters.

To get the length of the other piece, plug-in the value of x to 3/5x.

`3/5x=3/5(10)=3*2=6`

Thus, the length of the other piece is 6 meters.

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