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A mixture of 12 ounces of vinegar and oil is 40 percent vinegar,where all of the measurements are by weight. How many ounces of oil must be added to the mixture to produce a new mixture that is only 25 percent vinegar ?

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Step 1. Find out what is the weight of vinegar and the weight of oil in the initial mixture. Let's call them $m_{o}$ and $m_{v}$. You have that the $m_v$ is 40% of of the initial mixture, so $m_o$ is 60%

Step 2. In the final mixture you have only 25% vinegar, but the mass of vinegar did not change. You can calculate the total weight of the new mixture, $m_{final}$.

Step 3. Subtract the initial mass of the mixture

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The current mixture has $0.4(12)=4.8$ ounces of vinegar (and $7.2$ ounces of oil). You want to find the amount of extra oil $x$ such that $$\frac{4.8}{12+x}=0.25$$

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