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Yuki works at an aquarium. To clean a tank, she calculates (7)/(900) of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be 2(1)/(3)L of cleaning solution.
What is the total volume of the tank?

◻ liters

Yuki works at an aquarium. To clean a tank, she calculates $\frac{7}{900}$ of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be $2\frac{1}{3}$ $L$ of cleaning solution. $\newline$ What is the total volume of the tank? $\newline$ $\square$ liters

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Multi-step word problems

Full solution

Q. Yuki works at an aquarium. To clean a tank, she calculates

\frac{7}{900}

of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be

2\frac{1}{3}

L

of cleaning solution.

\newline

What is the total volume of the tank?

\newline

\square

liters

Convert to Improper Fraction: Yuki uses $(7)/(900)$ of the tank's volume for the cleaning solution, which equals $2(1)/(3)$ L. Convert $2(1)/(3)$ L to an improper fraction: $2(1)/(3) = (2 \times 3 + 1)/3 = (6 + 1)/3 = 7/3$ L.
Set Up Equation: Now, set up the equation $(7)/(900) \times \text{total\_volume} = 7/3$ . We need to find the $\text{total\_volume}$ .
Solve for Total Volume: To solve for $total\_volume$ , divide both sides by $(7)/(900)$ : $total\_volume = (\frac{7}{3}) / (\frac{7}{900})$ .
Simplify Right Side: Simplify the right side by multiplying by the reciprocal of $(7)/(900)$ : $\text{total\_volume} = (\frac{7}{3}) \times (\frac{900}{7})$ .
Cancel Out Sevens: The sevens cancel out, so $\text{total\_volume} = \frac{1}{3} \times 900$ .
Multiply to Find Total Volume: Multiply $\frac{1}{3}$ by $900$ to find the total volume: $\text{total\_volume} = \frac{900}{3}$ .
Calculate Total Volume: Calculate $900$ divided by $3$ : $\text{total\_volume} = 300$ .

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