Question

A photograph is $16$ inches long and has an area of $(16x+96)$ square inches. A custom-made frame is $2$ inches wide and costs $\$0.50$ per square inch. Write an expression that represents the cost of the frame

Answer 1

Hint: Area of rectangle = length $\times$ width

Step 1: Given that
Length of photograph = $16$ inches
Area of photograph = $(16x+96)$ sq. inches

First of all we will Factor out $16$ from the expression to find the width of the photograph.
$\left[16\right(x)+16(6\left)\right]=16(x+6)$

As are of photograph is = length $\times$ width
So by comparing, the width of the photograph is $(x+6)$ inches

Step 2: Now,

A custom-made frame is $2$ inches wide and costs $\$0.50$ per square inch.
The length of frame and photograph

$=16+2+2=20$inches
The width of the frame and photograph

$=(x+6+4)=x+10$inches
Area of the photograph and frame = length width
$=20(x+10)$

Step 3: Now

The area of only frame

= [(The area of photograph and frame) – (Area of photograph)]

$$\begin{gathered} =\left\{20\right(x+10)-(16x+96\left)\right\} \\ =20x+200-16x-96\{Distributiveproperty\} \\ =4x+104sqinches\{Combineliketerms\} \end{gathered}$$

Step 4: Now

The cost of frame is $\$0.50$ per square inch

And total area of frame we required $=4x+104$ sq inches
So, the cost of the frame is $[0.50\times (4x+104\left)\right]$

Final Answer: $[0.50\times (4x+104\left)\right]$