When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many kg

Question

4 years ago

5

of coffee are required to produce 100 cups of coffee?

2 answers:

Basile [38] · Answer 1 · 2022-03-01T04:27:36+03:00

5 0

we know that

$1\ pound=0.453592\ kg$

in this problem

a pound of coffee beans yields $50$ cups of coffee

so

by proportion

Find the kg of coffee that are required to produce $100$ cups of coffee

$\frac{0.453592}{50}\frac{kg}{cups} =\frac{x}{100}\frac{kg}{cups}\\ \\50*x=100*.453592\\ \\x =0.453592*100/50\\ \\x=0.907184\ kg$

therefore

<u>the answer is</u>

$0.907184\ kg$

defon · Answer 2 · 2022-03-01T06:11:16+03:00

It will require 0.91 kg of coffee beans to make 100 cups of coffee.

<h3>Further Explanation</h3>

Below are the steps needed to solve the problem:

Sort the given from the problem.
Calculate how many pounds of coffee beans are needed to make 100 cups of coffee.
Convert the pounds of coffee beans needed to kilograms.

STEP 1: The following relationships are stated in the problem:

Recall some additional conversion factor: 1 kg = 2.2 lbs.

STEP 2: Determine the mass (in pounds) of the coffee needed to make 100 cups:

$\frac{50 cups}{1 \ lb} = \frac{100 \ cups}{x}\\\\50x = 100\\\boxed {x= 2 lbs}$

STEP 3: Convert the pounds of coffee beans to kilograms using the conversion factor: 1 kg = 2.2 lbs

$mass \ of \ coffee \ beans \ = 2 \ lbs \times \frac{1 \ kg}{2.2 \ lbs}\\\\\boxed {mass \ of \ coffee \ beans \ = 0.9090 kg}$