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Read the description of a proportional relationship. $\newline$ Kurt owns and operates Stain-B-Gone Carpet Cleaners. He uses a special non-toxic cleaning solution to clean carpets. There is a proportional relationship between the amount of cleaning solution (in quarts) Kurt uses, $x$ , and the area of carpet (in square yards) he cleans with the solution, $y$ . $\newline$ Kurt uses $4$ quarts of cleaning solution to clean $12$ square yards of carpet. Write the equation for the relationship between $x$ and $y$ . $\newline$ $y = \_$

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Write and solve equations for proportional relationships

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Q. Read the description of a proportional relationship.

\newline

Kurt owns and operates Stain-B-Gone Carpet Cleaners. He uses a special non-toxic cleaning solution to clean carpets. There is a proportional relationship between the amount of cleaning solution (in quarts) Kurt uses,

x

, and the area of carpet (in square yards) he cleans with the solution,

y

.

\newline

Kurt uses

4

quarts of cleaning solution to clean

12

square yards of carpet. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Given Values: Step $1$ : Identify the given values and the relationship. $\newline$ Kurt uses $4$ quarts of cleaning solution to clean $12$ square yards of carpet. This gives us the ratio of quarts to square yards.
Calculate Constant: Step $2$ : Calculate the constant of proportionality, $k$ . To find $k$ , we divide the amount of carpet cleaned by the amount of solution used. $k = \frac{12 \text{ square yards}}{4 \text{ quarts}} = 3 \text{ square yards per quart}$ .
Write Proportional Equation: Step $3$ : Write the equation of the proportional relationship. $\newline$ Using the constant of proportionality, the relationship between $x$ (quarts) and $y$ (square yards) can be expressed as: $\newline$ $y = 3x$

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