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Students are making lemonade from a powdered lemon drink mix. Carlos mixes 2 cups of water and 3 teaspoons of powdered lemon mix. Sophie mixes 2 cups of water and 5 teaspoons of powdered lemon mix. Whose mix will be more lemony?
Carlos's mix will be more lemony.
Sophie's mix will be more lemony.
The two mixes will be equally lemony.

Students are making lemonade from a powdered lemon drink mix. Carlos mixes $2$ cups of water and $3$ teaspoons of powdered lemon mix. Sophie mixes $2$ cups of water and $5$ teaspoons of powdered lemon mix. Whose mix will be more lemony? $\newline$ Carlos's mix will be more lemony. $\newline$ Sophie's mix will be more lemony. $\newline$ The two mixes will be equally lemony.

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Counting principle

Full solution

Q. Students are making lemonade from a powdered lemon drink mix. Carlos mixes

2

cups of water and

3

teaspoons of powdered lemon mix. Sophie mixes

2

cups of water and

5

teaspoons of powdered lemon mix. Whose mix will be more lemony?

\newline

Carlos's mix will be more lemony.

\newline

Sophie's mix will be more lemony.

\newline

The two mixes will be equally lemony.

Analyze the problem: Analyze the problem. $\newline$ Carlos's mix: $2$ cups of water with $3$ teaspoons of lemon mix. $\newline$ Sophie's mix: $2$ cups of water with $5$ teaspoons of lemon mix. $\newline$ To determine which mix will be more lemony, we need to compare the ratio of lemon mix to water in each case.
Calculate Carlos's ratio: Calculate the ratio of lemon mix to water for Carlos. $\newline$ Carlos's ratio = Number of teaspoons of lemon mix / Number of cups of water $\newline$ Carlos's ratio = $3$ teaspoons / $2$ cups
Calculate Sophie's ratio: Calculate the ratio of lemon mix to water for Sophie. $\newline$ Sophie's ratio = Number of teaspoons of lemon mix / Number of cups of water $\newline$ Sophie's ratio = $5$ teaspoons / $2$ cups
Compare the ratios: Compare the ratios. $\newline$ A higher ratio of lemon mix to water means a more lemony mix. $\newline$ Carlos's ratio is $\frac{3}{2}$ , which simplifies to $1.5$ . $\newline$ Sophie's ratio is $\frac{5}{2}$ , which simplifies to $2.5$ . $\newline$ Since $2.5$ is greater than $1.5$ , Sophie's mix is more lemony.

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