Making Energy Drinks

Question

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.
You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and on the completeness and accuracy of your explanations.
Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy.
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 mixed energy drink? (2 points)

Answer 1

To find the ratio of drink mix to mixed energy drink, we first need to calculate the total amount of the mixed energy drink.

1. Total amount of the mixed energy drink:

   • Water: 8 cups
   • Drink mix: 3 cups
   • Total: \(8 + 3 = 11\) cups

2. Ratio of drink mix to mixed energy drink:

   • Drink mix: 3 cups
   • Mixed energy drink: 11 cups

Now, we can express this as a ratio:

\[ \text{Ratio of drink mix to mixed energy drink} = \frac{\text{drink mix}}{\text{mixed energy drink}} = \frac{3 \text{ cups}}{11 \text{ cups}} \]

Thus, the ratio of drink mix to mixed energy drink is \( \frac{3}{11} \) or \( 3:11 \).