A bakery makes two types of cookies: chocolate chip and oatmeal raisin. To make a batch of chocolate chip cookies, 2 cups of flour are needed. A batch of oatmeal raisin cookies requires 3 cups of flour. The bakery used 78 cups of flour in total to make 32 batches of cookies. How many batches of chocolate chip cookies were made? ______
Answer & Analysis
Analysis
Question Analysis
This problem involves making two types of cookie batches with different flour requirements, asking for the number of chocolate chip batches. It requires setting up a system of equations based on total batches and total flour used.
Key Concept Explanation
A system of linear equations uses two variables to represent the unknowns. Let c = batches of chocolate chip cookies, o = batches of oatmeal raisin cookies.
Step-by-step Solution
1. Define variables: c = chocolate chip batches, o = oatmeal raisin batches.
2. Equations:
Total batches: → (substitution).
Total flour: .
3. Substitute into the second equation:
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