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

Students are making lemonade from a powdered lemon drink mix. Jonathan mixes 33 cups of water and 22 teaspoons of powdered lemon mix. Sophia mixes 33 cups of water and 55 teaspoons of powdered lemon mix. Whose mix will be more watery?\newlineJonathan's mix will be more watery.\newlineSophia's mix will be more watery.\newlineThe two mixes will be equally watery.

Full solution

Q. Students are making lemonade from a powdered lemon drink mix. Jonathan mixes 33 cups of water and 22 teaspoons of powdered lemon mix. Sophia mixes 33 cups of water and 55 teaspoons of powdered lemon mix. Whose mix will be more watery?\newlineJonathan's mix will be more watery.\newlineSophia's mix will be more watery.\newlineThe two mixes will be equally watery.
  1. Analyze the problem: Analyze the problem.\newlineWe need to compare the concentration of the powdered lemon mix in the water for both Jonathan and Sophia. The concentration is determined by the ratio of powdered lemon mix to water.
  2. Calculate Jonathan's concentration: Calculate the concentration of Jonathan's mix.\newlineJonathan uses 22 teaspoons of powdered lemon mix for every 33 cups of water.\newlineConcentration of Jonathan's mix = (2teaspoons)/(3cups)(2 \, \text{teaspoons}) / (3 \, \text{cups})
  3. Calculate Sophia's concentration: Calculate the concentration of Sophia's mix.\newlineSophia uses 55 teaspoons of powdered lemon mix for every 33 cups of water.\newlineConcentration of Sophia's mix = (5teaspoons)/(3cups)(5 \, \text{teaspoons}) / (3 \, \text{cups})
  4. Compare concentrations: Compare the concentrations.\newlineA lower concentration of powdered lemon mix to water means the mix is more watery. Therefore, we compare the two ratios to see which is smaller.\newlineJonathan's concentration: 23\frac{2}{3}\newlineSophia's concentration: 53\frac{5}{3}\newlineSince 23\frac{2}{3} is less than 53\frac{5}{3}, Jonathan's mix is more watery.

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