Question

I need help with this word problem:
Army requirements call for 55 coffee grounds/quart of coffee. One barrel contains coffee with 67.5 grounds/quart and another contains coffee with 45/quart. How many quarts of each to make 18 quarts with the right amount of grounds?

Answer 1

Let's start by assigning the letter x to the amount of 67.5 grounds/qt coffee. Therefore (18-x) is the amount of 45 grounds/quart we'll use. Since we want 18 quarts of 55 ground/quart coffee, you'll want to multiply those two numbers. (See the keyword OF?) Set up the equation like so:
\[67.5x+45(18-x)=990\]
Using the distributive property, that will become
\[67.5x+810-45x=990\]
Subtract the 45x from the 67.5x.
\[22.5+810=990\]
Subtract 810 from both sides-
\[22.5=180\]
Divide 180 by 22.5.
\[180\div22.5=8\]
x=8
So we have 8 quarts of 67.5 ground/quart coffee and (18-8=10) 10 quarts of 45 ground/quart coffee. :)

Answer 2

Thank you so much- you're a superhero! :D

Answer 3

You're welcome! :D