Chapter 4, Problem 14PFA

a.

To determine

Find the length of the original plastic strip in inches.

Answer to Problem 14PFA

Plastic strip is 5 inches long.

Explanation of Solution

Given information:G cuts a plastic strip into two pieces, one of which 3 inches

longer than other .he then cuts the longer piece in half.Two of the three pieces are each 1 inch longer than the third piece

Calculation:

Let the original length of the plastic strip is x . x is cut in two pieces, if the length of one piece is y then length of other piece is $y+3$ .So,

  $\begin{array}{l}x=y+(y+3).\\ x=2y+\mathrm{3.......}(1)\end{array}$

Longer piece is $y+3$ again cuts in half that is $(y+3)/2$ each .So there are three piece $y,(y+3)/2\text{and}(y+3)/2$ .Two of the three pieces are each 1 inch longer than the third pieceso,

  $\begin{array}{l}(y+2)/2=y+1.\\ y+3=2y+2.\\ y=1.\\ \text{putting}y=1\text{in}\text{equation}(1).\\ x=2\times 1+3.\\ x=5.\\ \end{array}$

So, Plastic strip is 5 inches long

b.

To determine

Name the mathematical practice did you use to solve this problem.

Answer to Problem 14PFA

Linear equation practice use to solve this problem.

Explanation of Solution

Given information:G cuts a plastic strip into two pieces, one of which 3 inches longer than other .G then cuts the longer piece in half.Two of the three pieces are each 1 inch longer than the third piece

Calculation:

Let the original length of the plastic strip is x . x is cut in two pieces, if the length of one piece is y then length of other piece is $y+3$ .So,

  $\begin{array}{l}x=y+(y+3).\\ x=2y+\mathrm{3.......}(1)\end{array}$

Longer piece is $y+3$ again cuts in half that is $(y+3)/2$ each .So there are three piece $y,(y+3)/2\text{and}(y+3)/2$ .Two of the three pieces are each 1 inch longer than the third pieceso,

  $\begin{array}{l}(y+2)/2=y+1.\\ y+3=2y+2.\\ y=1.\\ \text{putting}y=1\text{in}\text{equation}(1).\\ x=2\times 1+3.\\ x=5.\\ \end{array}$

So, Plastic strip is 5 inches long

Linear equations of Algebra are used to solve this problem

Linear equation practice use to solve this problem.