Question

35 Points !

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.

Answer 1

For this case we have to:

x: It is the variable that represents the quantity of paint bottles

y: It is the variable that represents the number of boxes of colored pencils

So, we have:

`2x + 3.50y`

If you can not spend more than $ 42 then we have:

`2x + 3.50y\leq42`

Then you can buy 10 boxes of colored pencils and 3 of paint bottles at a cost of $ 41

`2 (3) +3.50 (10)\\6 + 35 = 41`

You can buy 5 boxes of colored pencils and 12 of paint bottles at a cost of $

`2 (12) +3.50 (5)\\24 + 17.5 = 41.5`

You can buy 7 boxes of colored pencils and 8 of paint bottles at a cost of $

`2 (8) +3.50 (7)\\16 + 24.5 = 40.5`

Answer:

`2x + 3.50y\leq42`