charlene is a video game designer and wants to make sure that her game can be played on all types of screens. In order for the games to work on both devices with a standard aspect ratio and those with widescreen aspect ratios, the playable area of the games should an aspect ratio of 3:2. This means that the width is equal to 3/2 times the height. On one type of tablet , the playable area of the game on the screen is 54 square inches. Write and solve a system of equations to determine the dimensions of the playable are. A) width=6 height=9B) width=6 height=4C) width=13.5 height=9D) width=9 height=6

The correct answer is D) width=9, height=6.

Let w represent the width and h represent the height.  The first equation we write deals with the area of the screen:
A=wh

Our playable area is 54, so we have
54=wh

Now we write the equation relating the width and the height.  The width is 3/2 times the height; this means
w=3/2h

We will use substitution to solve this.  Substitute the value for w from the second equation into the first equation:
54=wh
54=(3/2h)h
54=3/2h²

Divide both sides by 3/2:
54 ÷ 3/2 = 3/2h² ÷ 3/2
54/1 ÷ 3/2 = h²
54/1 × 2/3 = h²
108/3 = h²
36 = h²

Take the square root of both sides:
√36 = √h²
6 = h

The height is 6.  Substituting this into our first equation,
54=wh
54=w(6)

Divide both sides by 6:
54/6 = w(6)/6
9=w

The width is 9.