Question

if two quantities are proportional, then their relationship can be represented by an equation of the form $y = k \cdot x$\
(a) assume that the number of miles driven is proportional to the gas used by the car. if a car can drive 66 miles on 3 gallons of gas, find an equation that represents this relationship\
(b) assume that the water used in a pancake recipe is proportional to the flour used at a ratio of 6 cups of water to 7 cups of flour. find an equation that represents this relationship\
(c) assume that the ratio of currency a to currency b to currency c is 5 : 6 : 900 and that these currencies are proportional to each other. find equations that represent relationships between pairs of these quantities\
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(a) choose the correct answer below\
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\\(\bigcirc\\) a. $g = 66 \cdot m$\
\\(\bigcirc\\) b. $m = 22 \cdot g$\
\\(\bigcirc\\) c. $m = \frac{1}{22} \cdot g$\
\\(\bigcirc\\) d. $g = 22 \cdot m$

Explanation:

Step1: Determine the constant of proportionality

We know that the number of miles \( M \) is proportional to the gas \( G \) used, so \( M = k \cdot G \). Given that a car can drive 66 miles on 3 gallons of gas, we find \( k \) by \( k=\frac{M}{G}=\frac{66}{3} = 22 \).

Step2: Form the equation

Substituting \( k = 22 \) into the proportionality equation \( M = k\cdot G \), we get \( M = 22\cdot G \).

Answer:

B. \( M = 22\cdot G \)