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!
Page 2 | © Edgenuity Inc. 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. a) What is the ratio of water to drink mix? (2 points) b) What is the ratio of drink mix to water? (2 points) c) What is the ratio of drink mix to mixed energy drink? (2 points) d) What is the ratio of water to mixed energy drink? (2 points) Step 2: Testing Jerome’s brother’s approach 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. a) Complete the table below. (2 points) Original Ratio +1 +2 +3 +4 Drink mix (cups) 3 4 Water (cups) 8 9
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Page 4 | © Edgenuity Inc. Step 4: Calculating the right recipe for Jerome Twenty-two people are running in tomorrow’s road race and Jerome thinks they will each want two cups of energy drink. a) How many cups of energy drink does Jerome need to make? (1 point) b) How much water and how much drink mix should Jerome use to make enough energy drink for all the runners? Create a table to show your work and explain your results in writing. (4 points)
a) The ratio of water to drink mix is 8:3.
b) The ratio of drink mix to water is 3:8.
c) The ratio of drink mix to mixed energy drink is 3:11 (since Jerome uses 3 cups of drink mix and produces a total of 11 cups of energy drink).
d) The ratio of water to mixed energy drink is 8:11.
To test Jerome's brother's approach, we add one cup of water for every one cup of drink mix:
Original Ratio +1 +2 +3 +4
Drink mix (cups) 3 4 5 6
Water (cups) 8 9 10 11
a) Jerome needs to make a total of 22 * 2 = 44 cups of energy drink.
b) Using the approach suggested by Jerome's brother, we can calculate the amount of water and drink mix needed. Assuming the ratio remains the same, we can use proportions to find the amount of each ingredient needed:
Original Ratio: 8:3
Current Ratio: 11:3 (since we add 3 cups of drink mix)
Let x be the amount of drink mix needed to make 44 cups of energy drink.
Proportion:
8/3 = 44/x
8x = 3 * 44
8x = 132
x = 16.5
To maintain the ratio, Jerome needs to use 16.5 cups of drink mix. Based on the current ratio (11:3), he also needs to use 11/3 * 16.5 = 60.5 cups of water.
Therefore, Jerome should use 60.5 cups of water and 16.5 cups of drink mix to make enough energy drink for all the runners.