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Math  /  Algebra

QuestionOrly 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? 10 cups 2122 \frac{1}{2} cups 40 cups 3353 \frac{3}{5} cups

Studdy Solution

STEP 1

1. Orly uses 3 cups of raisins for every 10 cups of trail mix.
2. The amount of trail mix is directly proportional to the amount of raisins used.
3. We need to determine how many cups of trail mix are made if 12 cups of raisins are used.

STEP 2

1. Set up the proportion based on the given ratio.
2. Solve for the unknown quantity of trail mix.
3. Verify the solution and compare it to the given choices.

STEP 3

Set up the proportion based on the given ratio of raisins to trail mix.
Given: 3 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}}

STEP 4

Solve the proportion for x x .
Cross-multiplying gives: 3×x=12×10 3 \times x = 12 \times 10

STEP 5

Simplify the equation to solve for x x .
3x=120 3x = 120 x=1203 x = \frac{120}{3} x=40 x = 40

STEP 6

Verify the solution and compare it to the given choices.
Since x=40 x = 40 cups of trail mix, we check the options: - 10 cups - 2122 \frac{1}{2} cups - 40 cups - 3353 \frac{3}{5} cups
The correct answer is 40 cups.
The solution is 40 cups of trail mix.

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