System of Equations

Question

One 8-oz serving each of coffee, energy drink, and soda contains 200 mg of caffeine. One serving of coffee has 11 mg more caffeine than two servings of soda. One serving of energy drink contains 32 mg less caffeine than one serving each of coffee and soda. Find the amount of caffeine in one serving of each beverage. 

Answer 1

let x= soda; then coffee = 2x +11; energy = (soda + coffee) - 32 = (x + 2x +11) - 32

 

then 200mg = x + (2x + 11) + [x + 2x + 11 - 32]

 

then 200mg = 6x - 10, and x = 35mg

 

So, soda = 35mg, coffee = 2x + 11 = 81mg; energy = x + 2x + 11 - 32 = 84mg

 

Proof: 35mg + 81mg + 84mg = 200mg