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Home » 1/4 cup equals ounces - American Beagle Club

1/4 cup equals ounces - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 From (2): $ a + b + c = 3 $

📌 Multiply by 2: $ 2a + 2b + 2c = 6 $

📌 Subtract from (3):

📌 Multiply (2) by 3: $ 3a + 3b + 3c = 9 $

📌 Subtract from (4):

📌 Now from (5): $ b = 2 - 3a $

📌 Substitute into (6):

📌 12a + 3(2 - 3a) = 10 \Rightarrow 12a + 6 - 9a = 10 \Rightarrow 3a = 4 \Rightarrow a = \frac{4}{3}

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\(A \cap B \cap C = 0\) (impossible to have no types).
By inclusion-exclusion, the number of invalid configurations (missing...
|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \ca...
= 3 \cdot 512 - 3 \cdot 1 + 0 = 1536 - 3 = 1533
Thus, valid configurations with all three types present:
3^9 - 1533 = 19683 - 1533 = 18150
Therefore, the number of valid configurations is \(\boxed{18150}\).
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