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national society of high school scholars - Anadea

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Let \( x \) be the number of premium notebooks sold.

📌 The number of standard notebooks sold is \( x + 300 \).

📌 Since standard notebooks are 60% of the total sales, we have:

📌 x + 300 = 0.6(x + x + 300)

📌 Simplify the equation:

📌 x + 300 = 0.6(2x + 300)

📌 x + 300 = 1.2x + 180

📌 Rearrange to solve for \( x \):

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Divide by 4 to simplify:
x^2 + y^2 + rac{3}{4}z^2 + 2z - 4 = 0.
Now complete the square for $ z $:
rac{3}{4}z^2 + 2z = rac{3}{4}(z^2 + rac{8}{3}z) = rac{3}{4}\left( \...
ight)^2 - rac{16}{9}
ight) = rac{3}{4}\left(z + rac{4}{3}
ight)^2 - rac{4}{3}.
x^2 + y^2 + rac{3}{4}\left(z + rac{4}{3}
ight)^2 - rac{4}{3} - 4 = 0 \Rightarrow x^2 + y^2 + rac{3}{4}\left(z...
ight)^2 - rac{16}{3} = 0.

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