Question

Carmen can buy bottles of paint for $2.00 each and boxes of colored pencils for $3.50 each. She can spend no more than $42 on art supplies.

a. Write an inequality that shows how many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy.

b. Name three different solutions to the inequality.

Answer 1

Explanation:

Let x = the number of bottles of paint that Carmen can buy

Let y = the number of boxes of colored pencils that Carmen can buy

A bottle of paint costs $2

A box of colored pencils costs $3.50

She can spend no more than $42 on art supplies. This means

She can buy bottles of paint worth 2×x = $2x

She can buy boxes of colored pencils

worth 3.5 × y = $3.5y

Since the total amount she can spend cannot exceed $42, the equation becomes

2x + 3.5y lesser than or equal to 42

This is shown in the attached photo

b) three different solutions to the inequality would be three different possible values that x and y can take. These are

x = 7 while y = 8

x = 10 while y = 6

x = 14 and y = 4