Li Stuart
12/10/2023 · Senior High School
A cookie factory uses \( 3 / 4 \) of a bag of flour in each batch of cookies. The factory used \( 51 / 4 \) bags of flour yesterday. How many batches of cookies did the factory make? Write your answer as a fraction or as a whole or mixed number.
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Tutor-Verified Answer
Step-by-step Solution
To find out how many batches of cookies the factory made, we need to divide the total amount of flour used by the amount of flour used per batch.
The factory used \( \frac{51}{4} \) bags of flour yesterday, and each batch uses \( \frac{3}{4} \) of a bag of flour. We can set up the division as follows:
\[
\text{Number of batches} = \frac{\text{Total flour used}}{\text{Flour per batch}} = \frac{\frac{51}{4}}{\frac{3}{4}}
\]
To divide fractions, we multiply by the reciprocal of the divisor:
\[
\frac{\frac{51}{4}}{\frac{3}{4}} = \frac{51}{4} \times \frac{4}{3}
\]
Now, we can simplify this expression:
\[
= \frac{51 \times 4}{4 \times 3} = \frac{51}{3}
\]
Next, we perform the division:
\[
51 \div 3 = 17
\]
Thus, the factory made \( 17 \) batches of cookies.
The final answer is:
\[
\boxed{17}
\]
Quick Answer
The factory made 17 batches of cookies.
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