Sophia Posted May 6, 2008 Share Posted May 6, 2008 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. Quote Link to comment Share on other sites More sharing options...

eight_gregorys Posted May 6, 2008 Share Posted May 6, 2008 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! :) Quote Link to comment Share on other sites More sharing options...

Sophia Posted May 7, 2008 Author Share Posted May 7, 2008 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. Thanks for your help! Quote Link to comment Share on other sites More sharing options...

AngieW in Texas Posted May 7, 2008 Share Posted May 7, 2008 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. Quote Link to comment Share on other sites More sharing options...

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