Orly uses 3 cups of raisins for every 10 cups of trail mix she makes. How many cups of trail mix will she make if she uses 12 cups of raisins?
Answer (1)
We set up a proportion to relate the amount of raisins to the amount of trail mix. We are given that 3 cups of raisins are used for every 10 cups of trail mix. If Orly uses 12 cups of raisins, we find the corresponding amount of trail mix by solving the proportion 10 3 = x 12 for x . Cross-multiplying gives 3 x = 120 , and dividing by 3 gives x = 40 . Therefore, Orly will make 40 cups of trail mix.
Explanation
Understanding the Problem We are given that Orly uses 3 cups of raisins for every 10 cups of trail mix she makes. We need to find out how many cups of trail mix she will make if she uses 12 cups of raisins.
Setting up a Proportion We can set up a proportion to solve this problem. Let x be the number of cups of trail mix Orly will make if she uses 12 cups of raisins. The proportion is: cups of trail mix cups of raisins = 10 3 = x 12
Cross-Multiplying To solve for x , we can cross-multiply: 3 x = 10 × 12 3 x = 120
Solving for x Now, divide both sides by 3 to isolate x :
x = 3 120 x = 40
Final Answer Therefore, Orly will make 40 cups of trail mix if she uses 12 cups of raisins.
Examples
Understanding proportions is useful in many real-life situations. For example, if you are baking a cake and need to double the recipe, you can use proportions to determine the correct amount of each ingredient. Similarly, if you are traveling and want to convert kilometers to miles, you can use a proportion based on the conversion factor. Proportions help us scale quantities and maintain consistent relationships between them.
