A painter estimates that he uses 2 1/3 gallons of paint for every 500 square feet of wall space. If a project requires painting 1,750 square feet, how many gallons of paint will he need?
- A9 1/3 gallons
- B10 1/2 gallons
- C7 gallons
- D8 1/6 gallons
Show answer & explanationAnswer & explanation
Correct answer: D. 8 1/6 gallons
First, convert the mixed number to an improper fraction: 2 1/3 = 7/3 gallons. Next, find the paint usage per square foot: (7/3 gallons) / 500 sq ft = 7/1500 gallons/sq ft. Finally, multiply this rate by the total area to be painted: (7/1500 gallons/sq ft) * 1750 sq ft = (7 * 1750) / 1500 = 12250 / 1500. Simplify the fraction: 1225/150 = 245/30 = 49/6. Convert back to a mixed number: 49 / 6 = 8 with a remainder of 1, so 8 1/6 gallons.
Why the other options are wrong
- A. Incorrect. This would be the result if the usage was 2 2/3 gallons per 500 sq ft.
- B. Incorrect. This might be the result of various calculation errors or incorrect ratios.
- C. Incorrect. This might be the result of using 2 gallons per 500 sq ft.
Unit Rate with Mixed Numbers
Calculating a unit rate involves determining how much of one quantity corresponds to one unit of another quantity. When mixed numbers are involved, convert them to improper fractions or decimals for easier calculation.
- Convert mixed numbers to improper fractions or decimals.
- Set up a proportion or calculate the unit rate.
- Multiply the unit rate by the total quantity needed.
- Simplify fractions or convert back to mixed numbers for the final answer.
Memory trick: Mixed number to improper, find the rate, then multiply to seal your fate.