Question

caffeine content of different kinds of beverages
eight-ounce beverage | amount of caffeine (mg)
--- | ---
brewed coffee | 80–135
instant coffee | 65–100
espresso coffee (2 ounces) | 100
iced tea | 47
instant tea | 30
green tea | 15
hot cocoa | 14
the amount of caffeine varies greatly from product to product. examine a table comparing the caffeine content of a variety of drinks from caffeine table. examine the caffeine table, which compares the caffeine content of a variety of drinks.
leo drank 8 servings of iced tea and espresso beverages containing a total of 482 mg of caffeine. how many servings of espresso did he drink?

Explanation:

Step1: Define variables

Let \( x \) be the number of servings of espresso, and \( y \) be the number of servings of iced tea. We know that the total number of servings is 8, so \( x + y = 8 \), which means \( y = 8 - x \).

Step2: Set up caffeine equation

Each serving of espresso has 100 mg of caffeine, and each serving of iced tea has 47 mg. The total caffeine is 482 mg. So the equation is \( 100x + 47y = 482 \).

Step3: Substitute \( y \) into the equation

Substitute \( y = 8 - x \) into \( 100x + 47y = 482 \):
\[
100x + 47(8 - x) = 482
\]

Step4: Expand and simplify

\[
100x + 376 - 47x = 482
\]
\[
53x + 376 = 482
\]

Step5: Solve for \( x \)

Subtract 376 from both sides:
\[
53x = 482 - 376
\]
\[
53x = 106
\]
Divide both sides by 53:
\[
x = \frac{106}{53} = 2
\]

Answer:

Leo drank 2 servings of espresso.