20. 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

(a) The equality that express many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy is 2 x + 3.5 y = 42

b) Three different solutions:

x = 14, y = 4 is First Solution.

x = 7, y = 8 is Second Solution.

x = 21, y = 0 is Third Solution.

Step-by-step explanation:

Here, the cost of 1 bottle of paint = $2.00 each

The cost of 1 box of colored pencils = $3.5 each

Let us assume the number of bottle of paints purchased = x

So, the cost of x bottle of paints = x (Cost of 1 bottle of paint)

= x ($2.00) = 2 x

Also, assume the number of box of colored pencils purchased = y

So, the cost of y box of colored pencils = y (Cost of 1 box)

= y ($3.50) = 3.5 y

Also, the total amount to be spent on art supplies = $42

So, the total amount spent on x paint bottles + y box of colored pencil

= $42

or, 2 x + 3.5 y = 42

a) So, the equality that express many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy is 2 x + 3.5 y = 42

b) Three different solutions:

When y = 4, equation is: 2 x + 3.5 (4) = 42

or, 2 x = 42 - 14 = 28, or x = 28/2 = 14

So, x = 14, y = 4 is First Solution.

When y = 8, equation is: 2 x + 3.5 (8) = 42

or, 2 x = 42 - 28 = 14, or x = 14/2 = 7

So, x = 7, y = 8 is Second Solution.

When y = 0, equation is: 2 x + 3.5 (0) = 42

or, 2 x = 42, or x = 42/2 = 21

So, x = 21, y = 0 is Third Solution.