-) A picture is three times longer than its width. The frame around the picture is 5 inches wide.
Write an expression to help you find the area of the picture and the frame. (A=lw; A is area, I is
length, and w is width) Show all your work.

Step-by-step explanation:

To solve this problem, we  call:

L = length of the picture

w = width of the picture

We know that the picture is 3 times longer than its width, so

L = 3w (1)

Also, we know that the frame around the picture is 5 inches wide. This means that the length of the picture + frame is

L' = L + 5 + 5 (because there are 5 inches on one side and 5 inches on the other side of the picture), so

L' = L + 10

And similarly, the total width is

w' = w + 10

Therefore, the total area will be:

And using (1) we can rewrite it as

Solving explicitely,

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is