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Read the description of a proportional relationship. $\newline$ Alan's class is having a holiday party, and he is in charge of bringing juice. He decides to bring powdered juice mix and add water to it at school. There is a proportional relationship between the volume of water Alan uses to make the juice (in liters), $x$ , and the number of scoops of juice mix he uses, $y$ . $\newline$ To make the juice, Alan combines $4$ liters of water and $12$ scoops of juice mix. 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

Alan's class is having a holiday party, and he is in charge of bringing juice. He decides to bring powdered juice mix and add water to it at school. There is a proportional relationship between the volume of water Alan uses to make the juice (in liters),

x

, and the number of scoops of juice mix he uses,

y

.

\newline

To make the juice, Alan combines

4

liters of water and

12

scoops of juice mix. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Given Values: Step $1$ : Identify the given values from the problem. $\newline$ Alan uses $4$ liters of water for $12$ scoops of juice mix.
Determine Constant of Proportionality: Step $2$ : Determine the constant of proportionality ( extit{k}) by dividing the number of scoops by the volume of water. $\newline$ $k = \frac{12 \text{ scoops}}{4 \text{ liters}} = 3 \text{ scoops per liter}.$
Write Proportional Relationship Equation: Step $3$ : Write the equation representing the proportional relationship using the constant of proportionality. $\newline$ The equation is $y = 3x$ , where $y$ is the number of scoops and $x$ is the volume of water in liters.

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