To determine the total quarts of paint needed to paint two tables and eight chairs, let's break down the calculations step by step.
1. Calculate the amount of paint needed for the tables:
- Each table requires [tex]$1 \frac{5}{8}$[/tex] quarts of paint.
- There are 2 tables.
So, for the tables:
[tex]\[
2 \times \left(1 + \frac{5}{8}\right) = 2 \times 1 \frac{5}{8}
\][/tex]
Converting [tex]$1 \frac{5}{8}$[/tex] to an improper fraction:
[tex]\[
1 \frac{5}{8} = \frac{8}{8} + \frac{5}{8} = \frac{13}{8}
\][/tex]
Thus:
[tex]\[
2 \times \frac{13}{8} = \frac{26}{8} = 3.25 \text{ quarts}
\][/tex]
So, the total paint needed for the tables is [tex]\( 3.25 \)[/tex] quarts or [tex]\( 3 \frac{1}{4} \)[/tex] quarts.
2. Calculate the amount of paint needed for the chairs:
- Each chair requires [tex]$\frac{2}{3}$[/tex] quarts of paint.
- There are 8 chairs.
So, for the chairs:
[tex]\[
8 \times \frac{2}{3} = \frac{16}{3} = 5.\overline{3}3 \text{ quarts}
\][/tex]
This can be represented as approximately [tex]\( 5.333 \)[/tex] quarts.
3. Calculate the total amount of paint needed:
- Add the total quarts of paint for the tables and the chairs:
[tex]\[
3.25 + 5.333 = 8.583 \text{ quarts}
\][/tex]
Converting 8.583 into a more precise fractional form:
[tex]\[
8.583 = 8 + \frac{7}{12}
\][/tex]
So, the total paint needed is [tex]\( 8 \frac{7}{12} \)[/tex] quarts.
Therefore, the correct answer is:
[tex]\[
\boxed{8 \frac{7}{12}}
\][/tex]
So, you should bring [tex]\( 8 \frac{7}{12} \)[/tex] quarts of paint to complete this job.
