To find out how many cups of trail mix Orly will make if she uses 12 cups of raisins, we need to use the given ratio of raisins to trail mix. The ratio provided is 3 cups of raisins for every 10 cups of trail mix.
Let's follow these steps to solve the problem:
1. Identify the ratio: The problem states that the ratio of raisins to trail mix is 3:10. This means for every 3 cups of raisins, there are 10 cups of trail mix.
2. Set up the proportion: We can use this ratio to set up a proportion to find out how many cups of trail mix correspond to 12 cups of raisins. The proportion can be written as follows:
[tex]\[
\frac{3 \text{ cups of raisins}}{10 \text{ cups of trail mix}} = \frac{12 \text{ cups of raisins}}{x \text{ cups of trail mix}}
\][/tex]
3. Solve for [tex]\( x \)[/tex]: To find [tex]\( x \)[/tex], we set up the equation based on the proportion:
[tex]\[
\frac{3}{10} = \frac{12}{x}
\][/tex]
4. Cross multiply and solve: To solve for [tex]\( x \)[/tex], we cross multiply:
[tex]\[
3x = 12 \times 10
\][/tex]
5. Calculate the result: Now solve for [tex]\( x \)[/tex]:
[tex]\[
3x = 120
\][/tex]
[tex]\[
x = \frac{120}{3}
\][/tex]
[tex]\[
x = 40
\][/tex]
Therefore, Orly will make 40 cups of trail mix if she uses 12 cups of raisins.
