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Home » 128 Ounces Equal How Many Gallons? The Fast Math Surprise Series! - Decision Point

128 Ounces Equal How Many Gallons? The Fast Math Surprise Series! - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \[ (a - 2d) + (a + 2d) = 2a = 20 \Rightarrow a = 10. \]

📌 The second term is \( a - d = 10 - d \), and the fourth term is \( a + d = 10 + d \). Their product is:

📌 \[ (10 - d)(10 + d) = 100 - d^2 = 48. \]

📌 Solve for \( d^2 \):

📌 \[ 100 - d^2 = 48 \Rightarrow d^2 = 52. \]

📌 But we are asked for the third term, which is \( a = 10 \).

📌 \[\boxed{10}.\]1. A science educator is organizing a hands-on chemistry activity involving titration. She needs 0.5 liters of 0.2 M hydrochloric acid for each of 8 student groups. If she has a 2-liter stock solution of 1.0 M HCl, how many liters of water must she add to dilute the stock solution sufficiently for all groups?

📌 Each group requires 0.5 L × 0.2 mol/L = <<0.5*0.2=0.1>>0.1 moles of HCl.

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