Equivalent Ratios
Jerome makes and sells his own energy drinks. He mixes a liquid drink mix with water to create his own special blend.
Jerome usually uses 8 cups of water and 3 cups of drink mix. Tomorrow, there is a road race in town, however, and Jerome thinks he’ll be able to sell a lot more of his energy drinks than usual.
Jerome’s brother told him to add one cup of water for every one cup of drink mix he added to keep the ratio of water to drink mix the same and still increase the total amount of energy drink.
Jerome’s sister told him to multiply both the amount of water and the amount of drink mix by the same number to keep the ratio the same and still increase the total amount of energy drink.
Who is correct: Jerome’s brother or Jerome’s sister?
As you complete the task, keep this question in mind: Based on what you know about ratios, what do you think the answer will be?
Directions:
Complete each task, reading the directions carefully as you do.
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Now let’s get started!
Step 1: Finding the part-to-part and part-to-whole ratios
To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix.
What is the ratio of drink mix to water? (2 points)
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To find the ratio of drink mix to water, we can use the amounts that Jerome typically uses:
The ratio of drink mix to water is expressed as:
\[ \text{Ratio of drink mix to water} = \frac{\text{Cups of drink mix}}{\text{Cups of water}} = \frac{3}{8} \]
Thus, the ratio of drink mix to water is \(3:8\).
The ratio of drink mix to water is 3:8.
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