Question

One 8-oz serving each of coffee, energy drink, and soda contains 199 mg of caffeine. One serving of coffee has 11 mg more caffeine than two serving of soda. One serving of energy drink contains 33 less caffeine than one serving each of soda and coffee. Find the amount of caffeine in one serving of each beverage

Answer 1

One serving of soda contains 35 mg of caffeine, one serving of coffee contains 81 mg of caffeine, and one serving of energy drink contains 83 mg of caffeine.

Step-by-step explanation:

Let's solve this problem step by step:

• Let's assume the amount of caffeine in one serving of soda is x mg. Therefore, the amount of caffeine in two servings of soda is 2x mg.

• According to the information given, one serving of coffee has 11 mg more caffeine than two servings of soda. So, the amount of caffeine in one serving of coffee is 2x + 11 mg.

• The information also states that one serving of energy drink contains 33 mg less caffeine than one serving each of soda and coffee. Therefore, the amount of caffeine in one serving of energy drink is (x+2x + 11) - 33 mg.

To find the value of x, we can set up an equation:

• (x) + (2x + 11) + [(x+2x + 11) - 33] = 199

Simplifying the equation:

• 6x + 22 - 33 = 199

Combine like terms:

• 6x - 11 = 199

Add 11 to both sides:

• 6x = 210

Divide both sides by 6:

• x = 35

Therefore, one serving of soda contains 35 mg of caffeine. Substituting this value into the previous equations:

• One serving of coffee contains 2(35) + 11 = 81 mg of caffeine.

• One serving of energy drink contains 35+(2(35) + 11) - 33 = 83 mg of caffeine.

Answer 2

soda = 35mg

coffee = 81mg

energy = 83mg

Step-by-step explanation:

coffee + energy + soda = 199

coffee = 11 + (2 * soda)

energy = (soda + coffee) - 33

(11 + (2 * soda)) + ((soda + (11 + (2 * soda))) - 33) + soda = 199

11 + 2s + s + 11 + 2s - 33 + s = 199

22 + 6s - 33 = 199

-11 + 6s = 199

6s = 210

s = 35

soda = 35mg

c = 11 + 2s

c = 11 + 2(35)

c = 11 + 70

c = 81

coffee = 81mg

e = s + c - 33

e = (35) + (81) - 33

e = 116 - 33

e = 83

energy = 83mg