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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 of coffee are required to produce 100 cups of coffee?

Respuesta :

calculista

we know that

[tex]1\ pound=0.453592\ kg[/tex]

in this problem

a pound of coffee beans yields [tex]50[/tex] cups of coffee

so

by proportion

Find the kg of coffee that are required to produce [tex]100[/tex] cups of coffee

[tex]\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[/tex]

therefore

the answer is

[tex]0.907184\ kg[/tex]

mariejoepagaduan

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

Further Explanation

Below are the steps needed to solve the problem:

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

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

  • 1 pound of coffee beans = 50 cups of coffee
  • 4 cups = 1 quart

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:

[tex]\frac{50 cups}{1 \ lb} = \frac{100 \ cups}{x}\\\\50x = 100\\\boxed {x= 2 lbs}[/tex]

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

[tex]mass \ of \ coffee \ beans \ = 2 \ lbs \times \frac{1 \ kg}{2.2 \ lbs}\\\\\boxed {mass \ of \ coffee \ beans \ = 0.9090 kg}[/tex]

Therefore, 0.90 \ kg \ of \ beans are needed to make 100 cups of coffee.

Learn More

  • Learn More about Unit Conversion https://brainly.com/question/1594497
  • Learn More about Dimensional Analysis https://brainly.com/question/293494

Keywords: conversion, ratio and proportion

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