Question

Tucker is painting his pool deck over the weekend. The area of the deck is 76 1 2 square meters. He paints 2 3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch? Write your answer as a whole number, fraction, or mixed number. Simplify any fractions. square meters

Answer 1

To find out how many square meters Tucker has left to paint after lunch, we first need to calculate how much of the pool deck he has already painted.

1. **Calculate the area he has painted:**
\[
\text{Area of the deck} = 76 \frac{1}{2} \text{ square meters} = \frac{153}{2} \text{ square meters} \quad (\text{converting to an improper fraction})
\]
\[
\text{Area painted} = \frac{2}{3} \times \frac{153}{2} = \frac{2 \times 153}{3 \times 2} = \frac{153}{3} = 51 \text{ square meters}
\]

2. **Calculate the area left to paint:**
\[
\text{Area left} = \text{Area of the deck} - \text{Area painted} = 76 \frac{1}{2} - 51
\]
First, convert \( 76 \frac{1}{2} \) to an improper fraction:
\[
76 \frac{1}{2} = \frac{153}{2}
\]
Convert \( 51 \) to a fraction with a denominator of 2:
\[
51 = \frac{102}{2}
\]
Now, subtract:
\[
\text{Area left} = \frac{153}{2} - \frac{102}{2} = \frac{153 - 102}{2} = \frac{51}{2}
\]

3. **Convert back to a mixed number:**
\[
\frac{51}{2} = 25 \frac{1}{2}
\]

Thus, the area that Tucker has left to paint after lunch is:
\[
\boxed{25 \frac{1}{2}} \text{ square meters}
\]