Students are making lemonade from a powdered lemon drink mix. Adam mixes 3 cups of water and 4 cups of powdered lemon mix. Grace mixes 2 cups of water and 3 cups of powdered lemon mix. Use Adam and Grace’s percent of powdered lemon mix to determine whose mix will be more lemony.

Question

Answer
Attempt 1 out of 2

Adam percent of powdered lemon mix (to nearest whole number) =
%
Grace percent of powdered lemon mix (to nearest whole number) =
%

Answer 1

To find the percent of powdered lemon mix in Adam's and Grace's mixtures, we can use the formula:

\[ \text{Percent of powdered mix} = \left( \frac{\text{Amount of powdered mix}}{\text{Total volume}} \right) \times 100 \]

Adam's Mixture

• Amount of powdered lemon mix = 4 cups
• Amount of water = 3 cups
• Total volume = 3 cups (water) + 4 cups (powdered mix) = 7 cups

Now, we can calculate the percent of powdered lemon mix:

\[ \text{Percent of powdered mix (Adam)} = \left( \frac{4}{7} \right) \times 100 \approx 57.14% \]

Rounded to the nearest whole number:

\[ \text{Adam's percent of powdered lemon mix} \approx 57% \]

Grace's Mixture

• Amount of powdered lemon mix = 3 cups
• Amount of water = 2 cups
• Total volume = 2 cups (water) + 3 cups (powdered mix) = 5 cups

Now, we can calculate the percent of powdered lemon mix:

\[ \text{Percent of powdered mix (Grace)} = \left( \frac{3}{5} \right) \times 100 = 60% \]

Conclusion

Now we summarize the findings:

• Adam's percent of powdered lemon mix (to nearest whole number) = 57%
• Grace's percent of powdered lemon mix (to nearest whole number) = 60%

Comparison: Since Grace's mixture has a higher percentage of powdered lemon mix (60%) compared to Adam's (57%), Grace's mix will be more lemony.