QQuestionMathematics
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}}
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