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Orly has 33 cups of raisins for every 1010 cups of trail mix she makes. How many cups of trail mix will she make if she uses 1212 cups of raisins?

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Full solution

Q. Orly has 33 cups of raisins for every 1010 cups of trail mix she makes. How many cups of trail mix will she make if she uses 1212 cups of raisins?
  1. Set Proportion: Ratio of raisins to trail mix is 33 cups of raisins for every 1010 cups of trail mix. To find how many cups of trail mix Orly can make with 1212 cups of raisins, use the proportion:\newline3 cups of raisins10 cups of trail mix=12 cups of raisinsx cups of trail mix \frac{3 \text{ cups of raisins}}{10 \text{ cups of trail mix}} = \frac{12 \text{ cups of raisins}}{x \text{ cups of trail mix}}
  2. Cross-Multiply and Solve: Solve for x x by cross-multiplying:\newline3x=120 3x = 120 \newlinex=40 x = 40

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