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Tomas was able to fill 6(2)/(3) equalsized buckets with a total of 33(1)/(3) liters of paint. How much paint was in each whole bucket? liters

Tomas was able to fill 623 6 \frac{2}{3} equalsized buckets with a total of 3313 33 \frac{1}{3} liters of paint.\newlineHow much paint was in each whole bucket?\newlineliters

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Full solution

Q. Tomas was able to fill 623 6 \frac{2}{3} equalsized buckets with a total of 3313 33 \frac{1}{3} liters of paint.\newlineHow much paint was in each whole bucket?\newlineliters
  1. Identify total buckets and paint: Identify the total number of buckets and the total amount of paint used.\newlineTomas filled 6(23)6\left(\frac{2}{3}\right) buckets with a total of 33(13)33\left(\frac{1}{3}\right) liters of paint.
  2. Convert to improper fractions: Convert the mixed number for the buckets into an improper fraction to make the division easier.\newline6(23)6\left(\frac{2}{3}\right) can be converted to (6×3+2)/3=(18+2)/3=203\left(6 \times 3 + 2\right)/3 = \left(18 + 2\right)/3 = \frac{20}{3} buckets.
  3. Divide total paint by buckets: Convert the mixed number for the total amount of paint into an improper fraction. \newline33(13)33\left(\frac{1}{3}\right) can be converted to (33×3+1)/3=(99+1)/3=1003\left(33 \times 3 + 1\right)/3 = \left(99 + 1\right)/3 = \frac{100}{3} liters of paint.
  4. Simplify expression: Divide the total amount of paint by the number of buckets to find the amount of paint in each bucket.\newline(100/3)(100/3) liters ÷\div (20/3)(20/3) buckets = (100/3)×(3/20)(100/3) \times (3/20) = 100/3×3/20100/3 \times 3/20
  5. Divide by greatest common divisor: Simplify the expression by multiplying the numerators and denominators. 1003×320=(100×33×20)=30060\frac{100}{3} \times \frac{3}{20} = \left(\frac{100 \times 3}{3 \times 20}\right) = \frac{300}{60}
  6. Conclude bucket paint amount: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6060. \newline30060=5\frac{300}{60} = 5
  7. Conclude bucket paint amount: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6060. \newline30060=5\frac{300}{60} = 5 Conclude that each bucket contains 55 liters of paint.

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