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Ksju [112]
4 years ago
5

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?
Mathematics
2 answers:
Basile [38]4 years ago
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

defon4 years ago
5 0

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:

  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:

\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}

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

<h3>Learn More</h3>
  • Learn More about Unit Conversion brainly.com/question/1594497
  • Learn More about Dimensional Analysis brainly.com/question/293494

Keywords: conversion, ratio and proportion

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