Question

you are shopping for disposable cameras to hand out at a party. the daytime cameras costs 2.75 dollars and the flash camera costs 4.25 dollars. you must buy exactly 20 cameras and you want to spend between 65 and 75 dollars, inclusive. write and solve a compound inequality for this solution. list all of the solutions that involve whole numbers of cameras.

Answer 1

The solutions that involve whole numbers of cameras are (7, 13), (8, 12), (9, 11), (10, 10), (11, 9), (12, 8) and (13, 7)

Write and solve a compound inequality for this solution.

The given parameters are:

• Daytime cameras = $2.75
• Flash camera = $4.25
• Number of cameras = 20 cameras
• Amount spent = Between $65 and $75

Represent the daytime camera with x and the flash camera with y.

So, we have:

x + y = 20

65 <=2.75x + 4.25y <= 75

Make y the subject in x + y = 20

y = 20 - x

Substitute y = 20 - x in 65 <=2.75x + 4.25y <= 75

65 <=2.75x + 4.25(20 - x) <= 75

Expand

65 <=2.75x + 85 - 4.25x <= 75

This gives

65 <=-1.5x+ 85  <= 75

Subtract 85 from the inequality

-20 <=-1.5x <= -10

Split the inequality

-1.5x >= -20 and -1.5x <= -10

Divide by -1.5

x <= 13.33 and x >= 6.67

Combine the inequality

6.67 <= x <= 13.33

List all of the solutions that involve whole numbers of cameras.

In (a), we have:

6.67 <= x <= 13.33

This means that:

x = 7, 8, 9, 10, 11, 12, 13

Recall that:

y = 20 - x

So, we have:

y = 13, 12, 11, 10, 9, 8, 7

So, the solutions that involve whole numbers of cameras are (7, 13), (8, 12), (9, 11), (10, 10), (11, 9), (12, 8) and (13, 7)

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