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An electrician cuts a 136 ft long piece of cable. One piece is 16 feet less than 3 times the length of the other piece. Find the length of each piece.

Verified Answer :

texaschic101

x + y = 136
x = 3y - 16

3y - 16 + y = 136
4y - 16 = 136
4y = 136 + 16
4y = 152
y = 152/4
y = 38

x = 3y - 16
x = 3(38) - 16
x = 114 - 16
x = 98

the larger piece (x) = 98 ft and the smaller piece (y) = 38 ft

Length of the cable = 136 ft

Let the length of one piece be = x

Let the length of other piece be = y

The two equations formed are :

\(x+y=136\)    .... (1)

\(y=3x-16\)     ..... (2)

Solving the equation (1) by putting y=3x-16

\(x+3x-16=136\)

\(4x=136+16\)

\(4x=152\)

x=38 feet

\(y=3x-16\)

\(y=3(38)-16\)

\(y=114-16\)

y=98 feet feet

Hence, lengths of both the pieces are 38 feet and 98 feet.

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