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=9

B) width=6 height=4

C) width=13.5 height=9

D) 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.