Questions: 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 5/8 quarts of paint, and each chair requires 2/3 quarts of paint. How many total quarts of paint should you bring to paint this furniture?

Solution Steps

To determine the total amount of paint needed, we need to calculate the paint required for the tables and the chairs separately and then sum these amounts. Each table requires \(1 \frac{5}{8}\) quarts of paint, and each chair requires \(\frac{2}{3}\) quarts of paint. We will multiply the paint required per table by the number of tables and the paint required per chair by the number of chairs, and then add these two results together.

The amount of paint required for one table is given as \(1 \frac{5}{8}\) quarts. Converting this to an improper fraction, we have: \[ 1 \frac{5}{8} = \frac{13}{8} \] For two tables, the total paint required is: \[ 2 \times \frac{13}{8} = \frac{26}{8} = \frac{13}{4} \]

The amount of paint required for one chair is \(\frac{2}{3}\) quarts. For eight chairs, the total paint required is: \[ 8 \times \frac{2}{3} = \frac{16}{3} \]

Now, we need to sum the total paint required for both tables and chairs: \[ \text{Total Paint} = \frac{13}{4} + \frac{16}{3} \] To add these fractions, we need a common denominator. The least common multiple of 4 and 3 is 12. Converting both fractions: \[ \frac{13}{4} = \frac{39}{12}, \quad \frac{16}{3} = \frac{64}{12} \] Now, adding them together: \[ \frac{39}{12} + \frac{64}{12} = \frac{103}{12} \]

To express \(\frac{103}{12}\) as a mixed number: \[ \frac{103}{12} = 8 \frac{7}{12} \]

Final Answer