I downloaded worksheets from Kuta Software for more practice material. Systems of equations went well. Mixture problems required some Googling. Once I got a clearly worded example I was set. Everyone has a tendency to do it with things they understand well, but super math minds go all George Lucas when asked to explain their work.
What do you mean you don't see your motivation? It's right there. I wrote it.
When I got to the rate of work problems my decoder skills hung on through "calculate how long two people can do a job together if A works at x rate and B works at y rate. Then came "If A and B work together at x rate, and B works alone at y rate, how long will it take A to work alone?" It should be a simple matter of taking the equation I was already using and solving for a different variable.
And yet it is not proving so simple.
Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel 9 hours. Find how long it would take Paul to do it alone.
I set up my equation
(40 bushels / x hours) + (40 bushels / 9 hours) = (40 bushels / 4.95 hours)
My first thought it to cancel out all those 40s by multplying by 1/40, which gets me to
1/x + 1/9 = 1/4.95
Okay...I still have fractions. Which would be totally okay IF 1/4.95 didn't translate to .202020202.... Time for the homework helpers at algebra.com. (Tip: If you have a child enrolled in algebra who aces their homework but bombs tests, block this site and others like it. Actually just block it until you need to check their homework.)
One solution pulls the number 44.95 out of their Lucas machine, plugs it into the equation, and gets the answer. Where did that number come from?!?!?!?! Another solution explains it by having me multiply across the equation by 9(4.95). Which...I guess that makes sense because I want to get everything to a denominator of one. Why couldn't I see this yesterday? Ugh. The library computer is flashing that my session ends in ten minutes, so I'll skip the work and tell you the answer is 11.
Must post about inequalities before Monday. Must must must. Matrix starts Monday at all costs. Books are due February 8. Worst case scenario I check them out again once they hit the shelf. I doubt anyone wants to fight over algebra books.
Update: After my library session timed out I finally had that epiphany I was searching for. It wasn't multiply everything by 9(4.95). It was cross multiply everything by 9 * 4.95 * x, canceling out as appropriate. So yes, 44.55 came from somewhere, but I couldn't figure out how it went from one x to two.
For my own reference when Sue is having an algebra headdesk moment:
1/14/13 -- I just realized those equal signs in the middle should be multiplication signs. I spent so long trying to remember how to draw lines in Photoshop I forgot what kind of lines to draw! I'll fix them. Someday. Until then use your imagination.
equals 44.55
equals 4.95x
equals 9x
Update: After my library session timed out I finally had that epiphany I was searching for. It wasn't multiply everything by 9(4.95). It was cross multiply everything by 9 * 4.95 * x, canceling out as appropriate. So yes, 44.55 came from somewhere, but I couldn't figure out how it went from one x to two.
For my own reference when Sue is having an algebra headdesk moment:
1/14/13 -- I just realized those equal signs in the middle should be multiplication signs. I spent so long trying to remember how to draw lines in Photoshop I forgot what kind of lines to draw! I'll fix them. Someday. Until then use your imagination.
equals 44.55
equals 4.95x
equals 9x
SO
44.55 + 4.95x = 9x
44.55 = 4.05x
11 = x
Halle-frickin-llujah!
Somethings don't translate well from paperwork to computer notation. And for that there is Photoshop.
Crop tool only works on hands
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