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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 7900 \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 213 L 2 \frac{1}{3} \mathrm{~L} of cleaning solution.\newlineWhat is the total volume of the tank?\newlineliters

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Full solution

Q. Yuki works at an aquarium. To clean a tank, she calculates 7900 \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 213 L 2 \frac{1}{3} \mathrm{~L} of cleaning solution.\newlineWhat is the total volume of the tank?\newlineliters
  1. Convert to Improper Fraction: Convert the mixed number to an improper fraction. 2(13)2\left(\frac{1}{3}\right) L is the amount of cleaning solution Yuki adds to the tank, which is equal to (7900)\left(\frac{7}{900}\right) of the tank's total volume. First, we need to convert 2(13)2\left(\frac{1}{3}\right) to an improper fraction. 2(13)=(2×3+1)/3=(6+1)/3=732\left(\frac{1}{3}\right) = \left(2 \times 3 + 1\right)/3 = \left(6 + 1\right)/3 = \frac{7}{3} L
  2. Set Up Equation: Set up the equation to find the total volume of the tank.\newlineWe know that 73 L\frac{7}{3} \, \text{L} is 7900\frac{7}{900} of the tank's total volume. Let's call the total volume VV. So we can write the equation:\newline7900×V=73\frac{7}{900} \times V = \frac{7}{3}
  3. Solve for Total Volume: Solve for VV, the total volume of the tank.\newlineTo find VV, we need to divide both sides of the equation by (7)/(900)(7)/(900).\newlineV=(73)/(7900)V = (\frac{7}{3}) / (\frac{7}{900})
  4. Simplify Equation: Simplify the right side of the equation.\newlineWhen dividing fractions, we multiply by the reciprocal of the divisor. So we multiply 73\frac{7}{3} by the reciprocal of 7900\frac{7}{900}, which is 9007\frac{900}{7}.\newlineV=(73)×(9007)V = \left(\frac{7}{3}\right) \times \left(\frac{900}{7}\right)
  5. Compute Total Volume: Cancel out the common factors and compute the total volume.\newlineThe 7s7s cancel out, so we are left with:\newlineV=(1/3)×900V = (1/3) \times 900\newlineV=900/3V = 900/3\newlineV=300V = 300

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