Chapter 1.2, Problem 42STP

To determine

To find the measurement of longest piece of ribbon

Answer to Problem 42STP

Length of longest piece is 21 foot.

Explanation of Solution

Given information:

Length of ribbon= 36 foot.

Calculation:

Let the length of 2^nd piece of ribbon be x .

According to question,

Length of 1^st piece = $\frac{x}{2}$

Length of 3^rd piece= $1+2x$

As observed, 3^rd piece is longest. To find the length,

1^st + 2^nd+ 3^rd= 36

Substituting values,

  $\frac{x}{2}+x+1+2x=36$

Solving,

  $\frac{x}{2}+\frac{2x}{2}+\frac{2(1+2x)}{2}=36$

So,

  $\frac{x+2x+2(1+2x)}{2}=36$

Multiplying equation by 2,

  $7x+2=72$

Subtracting 2 from both sides,

  $7x=70$

Dividing by 7,

  $x=10$

Length of 3^rd piece= $1+2x$

Solving,

  = $1+2(10)$

Hence, length of longest piece is 21 foot.