And I'm Stuck

Word problems FTL.

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

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

No Wonder I Was Making Great Progress

I've been saying for days I was about to start the matrix, right? Monday night after I posted my blog, ate some cake, and pondered leaving my five year old on someone's doorstep (it was a bad Mama day) I cracked open Everything to practice what I've done so far. My planned quick practice turned into three hours of BWUH? because Everything just had to be written by someone just like my Algebra I teacher. I didn't close the book until 3:30 a.m.

Idiot's Guide is amazing at breaking things down, but so far it hasn't thrown the same type of trick problems at me. The things my teacher would've said, "I just taught you how to do this with an example -- apply what I just said to something that looks absolutely nothing like what we just did!" Fractions with equations in both the numerator and the denominator. Equations with mixed numerals. The dreaded word problems.

I knew it was all going too smoothly. I'll give myself this much -- I must understand what I'm doing now. I was able to figure out which concepts applied to the equations.


(5x - 4) / 7 = (2x + 9) / 3

I saw this and thought, "What the !@#$ am I supposed to do with this shenanigans? I guess I could make the denominators match."

[(3)(5x - 4) / (3)(7)] = [(7)(2x + 9) / (7)(3)]

(15x - 12) / 21 = (14x + 63) / 21

Multiply by the reciprocal to get rid of the denominators... while writing this I realized I could've just cross-multiplied the whole thing from jump street. This is what I get for doing algebra at 1:30 a.m. I can't believe I did all that extra work. And I did it for three different problems!!!!

15x - 12 = 14x + 63
x = 75



When I got to (2n + 9) / (5n - 2) = 1/3 I freaked out a little. Bearings were quickly restored via the long method. Let's try it the short way with cross-multiplication!

3(2n + 9) = 1(5n - 2)
6n + 27 = 5n - 2
n = -29

No algebra after midnight for me. I added three more steps to this.


The inequalities were really disappointing in Everything. No "less than/greater than or equal to" dilemmas at all. I flipped through and didn't see a section on them at all. Everything Guide to Algebra my rear. There was one answer that threw me. I won't bother with the whole process because I did get it right. The book gave the answer as -6 > x > -18. Idiot's Guide calls this bad math grammar and would have me write it -18 < x < -6. I like that better because it's ordered as the numbers appear on a number line. Is one considered technically correct? Technically correct is always the best kind of correct.

The matrix keeps getting shoved back, so I'm officially setting a new start date of 01/14/13 so I can get my posts about fighting with word problems and inequalities up and not do so much of this back and forth between concepts. Books have to be renewed by the 17th, so I have to finish these books three weeks after that. This will get interesting.