You work as a residential painter. A customer wants two tables and eight chairs painted using one coat of the same color paint. Each table requires $1 \frac{5}{8}$ quarts of paint, and each chair requires $\frac{2}{3}$ quarts of paint. How many total quarts of paint should you bring to paint this furniture?
A. $6 \frac{23}{24}$
B. $8 \frac{7}{12}$
C. $5 \frac{1}{3}$
D. $3 \frac{1}{4}$
E. $3 \frac{9}{11}$
Answer (2)
Convert the mixed number to an improper fraction: 1 8 5 = 8 13 .
Calculate the total paint for the tables: 2 × 8 13 = 4 13 .
Calculate the total paint for the chairs: 8 × 3 2 = 3 16 .
Add the paint for the tables and chairs and convert to a mixed number: 4 13 + 3 16 = 12 103 = 8 12 7 .
8 12 7
Explanation
Problem Analysis We need to calculate the total amount of paint required to paint two tables and eight chairs. Each table needs 1 8 5 quarts of paint, and each chair needs 3 2 quarts of paint.
Convert Mixed Number to Improper Fraction First, let's convert the mixed number 1 8 5 to an improper fraction: 1 8 5 = 8 1 × 8 + 5 = 8 8 + 5 = 8 13 So, each table requires 8 13 quarts of paint.
Calculate Paint for Tables Now, calculate the total paint needed for the two tables: 2 × 8 13 = 8 2 × 13 = 8 26 = 4 13 So, the tables need 4 13 quarts of paint.
Calculate Paint for Chairs Next, calculate the total paint needed for the eight chairs: 8 × 3 2 = 3 8 × 2 = 3 16 So, the chairs need 3 16 quarts of paint.
Calculate Total Paint Now, add the total paint needed for the tables and the chairs: 4 13 + 3 16 = 4 × 3 13 × 3 + 3 × 4 16 × 4 = 12 39 + 12 64 = 12 39 + 64 = 12 103 So, the total paint needed is 12 103 quarts.
Convert Improper Fraction to Mixed Number Finally, convert the improper fraction 12 103 to a mixed number: 12 103 = 8 12 7 So, the total paint needed is 8 12 7 quarts.
Final Answer Therefore, you should bring 8 12 7 quarts of paint to paint the furniture.
Examples
When planning a home renovation project, calculating the amount of materials needed is crucial for budgeting and efficiency. For instance, if you're tiling a bathroom, you need to calculate the area to be tiled and the number of tiles required, considering waste from cuts. Similarly, when landscaping, you need to determine the volume of soil or mulch needed for a garden bed. Accurate calculations prevent overspending and minimize waste, ensuring a smooth and cost-effective project.
You need a total of 8 12 7 quarts of paint to paint the two tables and eight chairs. This was calculated by determining the individual paint required for each piece of furniture and then summing the total amounts. The correct answer is option B: 8 12 7 .
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