Charlene is a video game designer and wants to make sure that her games 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 have an aspect ratio of 3: 2. this means that the width is equal to 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 area. a. the playable area has a width of 6 inches and a height of 4 inches. b. the playable area has a width of 6 inches and a height of 9 inches. c. the playable area has a width of 9 inches and a height of 6 inches. d. the playable area has a width of 13.5 inches and a height of 9 inches.

C. The playable area has a width of 9 inches and a height of 6 inches.

There are a number of ways you can get there.

1. Check the answers to see which have the right area and aspect ratio.

2. If the screen were 3:2 (inches), its area would be 6 in². The area of 54 in² is 9 times that value, so the actual screen dimensions are √9 = 3 times 3:2. That is, they are width:height = 9:6 inches — matches selection C.

3. You can write equations for width and height and solve.

Substituting w=3/2·h into the second equation gives

... (3/2)h·h = 54

... h² = 36 . . . . . multiply by 2/3

... h = √36 = 6 . . . . square root, result in inches . . . . matches selection C

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.