# algebra problem

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because y'all are so smart and I'm not:tongue_smilie:

The cooks have one barrel of coffee with 67.5 grounds per quart in it and another barrel with 45 grounds per quart. How many quarts of each should they mix together to make up 18 quarts with 55 grounds per quart of coffee in it?

I have the answer (scroll down), but can't figure out how to set up the problem.

tia!

8 quarts of the 6.75 grounds/quart and 10 quarts of the 45 grounds/quart.

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Okay, I figured it out. I hope I can explain it properly.

x + y = 18 (The number of total quarts)

To solve for this, set up the problem like this:

67.5x + 45y=990 (I got 990 from multiplying the total number of grounds.)

Substitute 18 - x for y. This will allow you solve for y.

67.5x + 45(18-x) = 990

67.5x + 810 - 45x = 990 (subtract 67.5x - 45x)

22.5x + 810 = 990 (subtract 810 from both sides)

22.5x = 180 (divide both sides by 22.5)

x = 8

Plug that into x + y = 18

8 + y = 18 (subtract 8 from both sides)

y = 10

I hope I didn't confuse you in explain this. It's one of those things I know "how" to do, but have a hard time explaining.

Happy Algebra! :)

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Aha!

We had the 67.5x+45(18-x) part, but we didn't know what to make it equal!

This problem was making me crazy all day.

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My 7th grader hates that type of problem. She just finished the "solving systems of equations" chapter in Kinetic Books Algebra and now she's doing that exact same chapter in Jacobs. She wasn't happy that they two programs happened to coincide this time. The problems like the one you typed up are the only ones she had trouble with.

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