This is really simple algebra but it actually happened to me within the last few days.
Somebody walked into my office and said "My bill after tax was $508.00 and the tax rate is 6%. How do I figure out what the original charge was?"
So:
"An unknown number plus 6% of that unknown number is 508."
x + .06x = 508 (express the problem)
1.06x = 508 (combine the terms)
1.06x / 1.06 = 508 / 1.06 (isolate the variable)
x = 479.25 (solve for the variable)
"The unknown number is $479.25."
I hope some math genius will tell me that's right and there's no simpler way to do it.
508/1.06 = 479.25
Same exact problem, shortcutted, without introducing the letters. To underwhy it works, you need to use the breakdown like you did.
This is the kind of grocery store algebra people use every day (IF THEY DON'T WANT TO GET SCREWED!) and hardly even realize it.
You got the right answer, the right way. People with more sophistication would tend to do some of the steps in their head, is all. Algegra is just a formal, systematic way of solving "word problems."I was different from my classmates in grammar school; if the homework assignment in arithmetic was a page of number crunching, we'd all groan together. But if it was a page of "word problems," the rest of the class would really groan but I would rejoice: "Hey, only six problems! And the interesting kind, at that!"
I became an engineer - and more mathematically inclined than many other engineers, at that. I would however be diffident about claiming that one cannot have a succesful life without algebra. After all, people were having successful lives before algegra was invented!
Actually, the easiest way is to just look at the receipt. ;) If that option isn't possible then, yes you did it correctly.
Why is it I just can't grab my calulator and say: 508.00 minus 6%? You would think I would get the right number....
What is 479.25 + 6%? and get the right answer?
Personally ~~I think the calculators are defective. Probably made in Taiwan or China.