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?
Tucker paints 2/3 * 76 = <<2/3*76=50.666666666666664>>50.67 square meters before stopping for lunch.
After lunch, Tucker has 76 - 50.67 = <<76-50.67=25.33>>25.33 square meters left to paint. Answer: \boxed{25.33}.
To find out how many square meters Tucker has left to paint after lunch, we need to calculate the area of the deck that he has already painted before lunch.
Given that the total area of the deck is 76 1/2 square meters, and Tucker has painted 23/30 (2/3) of the deck before lunch, we can calculate the area he has already painted.
Area painted = (23/30) * (76 1/2) square meters
To calculate this, let's first convert the mixed number 76 1/2 to an improper fraction:
76 1/2 = (76 * 2 + 1) / 2 = 153/2
Now, we can substitute these values into our formula:
Area painted = (23/30) * (153/2) square meters
To multiply fractions, we multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator:
Area painted = (23 * 153) / (30 * 2) square meters
Simplifying this fraction gives us:
Area painted = 3498/60 square meters
Now, if we subtract the area painted from the total area of the deck, we can find out how many square meters Tucker has left to paint after lunch:
Area left to paint = Total area - Area painted
Area left to paint = 76 1/2 - 3498/60 square meters
To subtract fractions, we need a common denominator. In this case, the denominator is 2 * 60 = 120. Therefore, we convert 76 1/2 to a fraction with a denominator of 120:
76 1/2 = (76 * 2 + 1) / 2 = 153/2
Now we can subtract the fractions:
Area left to paint = (153/2) - (3498/60) square meters
To subtract fractions, we need to have the same denominator. Therefore, we need to multiply the numerator and denominator of (153/2) by 60, and the numerator and denominator of (3498/60) by 2:
Area left to paint = (153 * 60) / (2 * 60) - (3498 * 2) / (60 * 2) square meters
Simplifying this expression gives us:
Area left to paint = 9180/120 - 6996/120 square meters
Now, we can subtract the fractions:
Area left to paint = (9180 - 6996) / 120 square meters
Simplifying this expression gives us:
Area left to paint = 2184/120 square meters
Since this is an improper fraction, we can simplify it to a mixed number:
Area left to paint = 18 and 24/120 square meters
Simplifying this mixed number further gives us:
Area left to paint = 18 and 1/5 square meters
Therefore, Tucker has 18 1/5 square meters left to paint after lunch.