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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 $6 \frac{2}{3}$ equalsized buckets with a total of $33 \frac{1}{3}$ liters of paint. $\newline$ How much paint was in each whole bucket? $\newline$ liters

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GCF and LCM: word problems

Full solution

Q. Tomas was able to fill

6 \frac{2}{3}

equalsized buckets with a total of

33 \frac{1}{3}

liters of paint.

\newline

How much paint was in each whole bucket?

\newline

liters

Identify total buckets and paint: Identify the total number of buckets and the total amount of paint used. $\newline$ Tomas filled $6\left(\frac{2}{3}\right)$ buckets with a total of $33\left(\frac{1}{3}\right)$ liters of paint.
Convert to improper fractions: Convert the mixed number for the buckets into an improper fraction to make the division easier. $\newline$ $6\left(\frac{2}{3}\right)$ can be converted to $\left(6 \times 3 + 2\right)/3 = \left(18 + 2\right)/3 = \frac{20}{3}$ buckets.
Divide total paint by buckets: Convert the mixed number for the total amount of paint into an improper fraction. $\newline$ $33\left(\frac{1}{3}\right)$ can be converted to $\left(33 \times 3 + 1\right)/3 = \left(99 + 1\right)/3 = \frac{100}{3}$ liters of paint.
Simplify expression: Divide the total amount of paint by the number of buckets to find the amount of paint in each bucket. $\newline$ $(100/3)$ liters $\div$ $(20/3)$ buckets = $(100/3) \times (3/20)$ = $100/3 \times 3/20$
Divide by greatest common divisor: Simplify the expression by multiplying the numerators and denominators. $\frac{100}{3} \times \frac{3}{20} = \left(\frac{100 \times 3}{3 \times 20}\right) = \frac{300}{60}$
Conclude bucket paint amount: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $60$ . $\newline$ $\frac{300}{60} = 5$
Conclude bucket paint amount: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $60$ . $\newline$ $\frac{300}{60} = 5$ Conclude that each bucket contains $5$ liters of paint.

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