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For a drink recipe, the amount of carrot juice is proportional to the amount of guava juice. This equation represents the proportional relationship between the number of quarts of carrot juice $c$ and guava juice $g$ in a recipe. $3c=4g$ How many quarts of carrot juice would be used with $1$ quart of guava juice?

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Evaluate two-variable equations: word problems

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Q. For a drink recipe, the amount of carrot juice is proportional to the amount of guava juice. This equation represents the proportional relationship between the number of quarts of carrot juice

c

and guava juice

g

in a recipe.

3c=4g

How many quarts of carrot juice would be used with

1

quart of guava juice?

Understand Proportional Relationship: Understand the given proportional relationship. $\newline$ The equation $3c = 4g$ represents the relationship between the amount of carrot juice ( $c$ ) and guava juice ( $g$ ). This means that for every $3$ quarts of carrot juice, there are $4$ quarts of guava juice.
Set Up Equation for $g=1$ : Set up the equation to solve for $c$ when $g$ is $1$ quart. $\newline$ We need to find the value of $c$ when $g$ is $1$ quart. So we substitute $g$ with $1$ in the equation $3c = 4g$ . $\newline$ $c$ $0$
Solve for c: Solve for c. $\newline$ Now we solve the equation for $c$ . $\newline$ $3c = 4$ $\newline$ $c = \frac{4}{3}$ $\newline$ $c = 1.333\ldots$
Interpret Result: Interpret the result. $\newline$ Since we cannot have a fraction of a quart in this context, we interpret the result as approximately $1.33$ quarts of carrot juice for every quart of guava juice.

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