Chapter 4.6, Problem 16PPS

To determine

To find: The width of the door

Answer to Problem 16PPS

The width of the door is 3 ft.

Explanation of Solution

Given:

The height of the door is 1 foot more than twice its width.

Door is 7 feet high

Calculation:

Let w be the width of the door.

Twice of the width means 2w.

Given that the height h of the door is 1 foot more than twice its width.

One foot more than twice of the width means 1 + 2w.

Thus, h =1+2w.

Here, door is 7 feet high, thatis, h =7 ft.

Putting all together, the required equation is,

  $1=2w=7\mathrm{.....}\text{(1) }$

Find the width w.

Solve the equation (1) for w.

  $\begin{array}{l}1+2w=7\\ 1+2w-1=7-1\text{ Subtraction property of equality}\\ 2w=6\text{ Simplify}\\ \frac{2w}{2}=\frac{6}{2}\text{ Division Property of equality}\\ w=3\text{ Simplify}\end{array}$

Hence, the width of the door is 3ft.

Conclusion:

Hence, the width of the door is 3ft.