A chef has a large container full of olive oil. In one night, after he used $25$ quarts of olive oil, $35.9 \%$ of the full container of olive oil remained. To the nearest whole quart, how many quarts of olive oil remained in the container?

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Q. A chef has a large container full of olive oil. In one night, after he used

25

quarts of olive oil,

35.9 \%

of the full container of olive oil remained. To the nearest whole quart, how many quarts of olive oil remained in the container?

Problem Understanding: Understand the problem and identify what is given and what needs to be found. $\newline$ We know that after using $25$ quarts of olive oil, $35.9\%$ of the oil remains in the container. We need to find out the total amount of olive oil that was in the container before the chef used any, and then calculate how much remains.
Expressing Percentage as Decimal: Express the remaining percentage of olive oil as a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $35.9\%$ as a decimal is $\frac{35.9}{100} = 0.359$ .
Total Amount of Olive Oil: Let the total amount of olive oil in the container before the chef used any be $x$ quarts. $\newline$ After using $25$ quarts, $35.9\%$ of $x$ is left. $\newline$ So, $0.359 \times x =$ amount of olive oil remaining.
Setting up the Equation: Set up the equation to find the total amount of olive oil before any was used. $\newline$ Since $25$ quarts were used and $35.9\%$ remains, we can say that $100\% - 35.9\% = 64.1\%$ of the oil was used. $\newline$ Therefore, $64.1\%$ of ' $x$ ' is equal to the $25$ quarts used. $\newline$ Convert $64.1\%$ to a decimal to get $0.641$ . $\newline$ So, $0.641 \times x = 25$ .
Solving for $x$ : Solve the equation for $x$ to find the total amount of olive oil in the container before any was used. $\newline$ Divide both sides of the equation by $0.641$ to isolate $x$ . $\newline$ $x = \frac{25}{0.641}$ $\newline$ Calculate the value of $x$ . $\newline$ $x \approx 39.00156$ quarts $\newline$ $x \approx 39$ quarts
Calculating Remaining Oil: Calculate the amount of olive oil remaining after the chef used $25$ quarts. $\newline$ We already know that $35.9\%$ of $x$ remained, and we have found $x$ to be approximately $39$ quarts. $\newline$ So, $0.359 \times 39 \approx 14.001$ quarts.
Rounding to Nearest Quart: Round the result to the nearest whole quart as the problem asks for the answer to the nearest whole quart. $\newline$ The amount of olive oil remaining is approximately $14$ quarts when rounded to the nearest whole quart.