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Math  /  Numbers & Operations

QuestionMargaret uses 1341 \frac{3}{4} teaspoons of key lime zest to make 12 key lime cupcakes. She wants to make 30 cupcakes. How much key lime zest will Margaret use?

Studdy Solution

STEP 1

1. Margaret uses 1341 \frac{3}{4} teaspoons of key lime zest for 12 cupcakes.
2. The amount of zest used is directly proportional to the number of cupcakes.
3. Margaret wants to make 30 cupcakes.

STEP 2

1. Convert the mixed number to an improper fraction.
2. Set up a proportion based on the number of cupcakes.
3. Solve the proportion to find the amount of zest needed for 30 cupcakes.

STEP 3

Convert the mixed number 1341 \frac{3}{4} to an improper fraction.
134=4×1+34=74 1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}

STEP 4

Set up a proportion to find the amount of zest needed for 30 cupcakes.
74 teaspoons12 cupcakes=x teaspoons30 cupcakes\frac{\frac{7}{4} \text{ teaspoons}}{12 \text{ cupcakes}} = \frac{x \text{ teaspoons}}{30 \text{ cupcakes}}

STEP 5

Write the proportion.
74×12=x30 \frac{7}{4 \times 12} = \frac{x}{30}

STEP 6

Solve the proportion by cross-multiplying.
30×74×12=x 30 \times \frac{7}{4 \times 12} = x
x=30×74×12 x = \frac{30 \times 7}{4 \times 12}

STEP 7

Calculate the amount of zest needed for 30 cupcakes.
x=21048 x = \frac{210}{48}
Simplify the fraction:
x=358 x = \frac{35}{8}
Convert to a mixed number:
x=438 x = 4 \frac{3}{8}
Margaret will use:
438 teaspoons\boxed{4 \frac{3}{8} \text{ teaspoons}}

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