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Olivia is painting a logo for a billboard and wants to use a combination of blue paint and red paint to completely cover a 5000 square foot billboard. A gallon of paint can cover 500 square feet. Red paint costs $20 per gallon and blue paint costs $30 per gallon. She only has $250 to spend. Write a system of inequalities that can be used to show all the possible combinations of paint that meet her goals.

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Answer:

($20/gal)r + ($30/gal)b ≤ $250

r + b ≤ 10 (gallons)

Step-by-step explanation:

Represent the amount of red paint by r and that of blue point by b.

Olivia must cover 5000 ft^2 with paint, which comes out to 5000/500, or 10, gallons total of red and blue paint.  The corresponding inequality is

r + b ≤ 10 (gallons)

She has onlyl $250 to spend.  Therefore, the following must hold true:

($20/gal)r + ($30/gal)b ≤ $250

The required sysstem of inequalities is thus

($20/gal)r + ($30/gal)b ≤ $250

r + b ≤ 10 (gallons)

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