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QuestionMathematics

a) Four gallons of water weigh 33.4 lb. How much do 7.5 gallons of water weigh? b) Four gallons of water weigh 33.4 lb. Find the constant of variation.
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Answer

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Step 1:
I'll solve this problem step by step, following the specified LaTeX formatting guidelines:

Part a) Weight of 7.5 Gallons of Water

Step 2:
: Set up the proportion

\frac{33.4 \text{ lb}}{4 \text{ gallons}} = \frac{x \text{ lb}}{7.5 \text{ gallons}}
Let's use the given information that 4 gallons weigh 33.4 lb to find the weight of 7.5 gallons.

Step 3:
: Cross multiply

33.4 \times 7.5 = 4x

Step 4:
: Solve for x

x = \frac{33.4 \times 7.5}{4}

Step 5:
: Calculate the final weight

x = \frac{250.5}{4} = 62.625 \text{ lb}

Final Answer

Part b) Constant of Variation Step 1: Identify the relationship The relationship between gallons and weight follows the form y = kx, where k is the constant of variation. Step 2: Calculate the constant k = \frac{33.4 \text{ lb}}{4 \text{ gallons}} = 8.35 \frac{\text{lb}}{\text{gallon}}