To find out how many tablespoons of kernels Sernina needs to make 6 cups of popcorn, we first need to determine the ratio of popcorn made to the number of tablespoons of kernels used.
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Convert mixed numbers to improper fractions:
- \( 2 \frac{1}{4} \) cups can be converted as follows: \[ 2 \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ cups} \]
- \( 1 \frac{1}{2} \) tablespoons can be converted as follows: \[ 1 \frac{1}{2} = \frac{3}{2} \text{ tablespoons} \]
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Determine the ratio of popcorn to kernels:
- The ratio of cups of popcorn to tablespoons of kernels is: \[ \text{Ratio} = \frac{\frac{9}{4} \text{ cups}}{\frac{3}{2} \text{ tablespoons}} = \frac{9}{4} \times \frac{2}{3} = \frac{9 \times 2}{4 \times 3} = \frac{18}{12} = \frac{3}{2} \]
- This means that for every \( \frac{3}{2} \) tablespoons of kernels, Sernina makes \( \frac{9}{4} \) cups of popcorn.
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Calculate how many tablespoons are needed for 6 cups:
- Now we need to find how many tablespoons correspond to 6 cups of popcorn: \[ \frac{9}{4} \text{ cups corresponds to } \frac{3}{2} \text{ tablespoons} \]
- To find how many tablespoons \( x \) are needed for 6 cups, we set up the ratio: \[ \frac{9/4}{3/2} = \frac{6}{x} \]
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Cross multiply to solve for \( x \): \[ (9/4)x = (3/2)(6) \]
- Calculate the right side: \[ (3/2) \times 6 = \frac{18}{2} = 9 \]
- Now set up the equation: \[ \frac{9}{4}x = 9 \]
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Isolate \( x \): \[ x = 9 \times \frac{4}{9} = 4 \]
Thus, Sernina needs 4 tablespoons of kernels to make 6 cups of popcorn.
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