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Basics of Algebra: Part V

Algebra, part V- real algebra


This series of lessons is designed to help you learn, or review, the fundamentals of algebra. It’s time to see how algebra relates to real life.

Real algebra, as we’ve already seen, can help you solve equations. But most people don’t encounter many situation where a stranger with a gun tells you “Solve this quadratic equation or die!”. What is this actually useful for?

Modeling real-life situations using equations

Yes, unsurprisingly, we can translate real life problems into math, and solve them. First things first though- the real basic relations and how they translate to basic operations:

Words Example Symbol Math
Is/equals The number of pickles in the jar is 5 ” = “ P=5
More than Max have 3 cars more than Frankie ” + “ M=F+3
Less than John bought 4 less apples than usual ” – “ J=U-4
Of Half of my friends are evil ” * “ E=\frac{1}{2} * F
For Jack got 2 prizes for every every 6 prizes Tom got ” / “ J=\frac{6T}{2}

See how easy this is? translating simple stuff into equations is a real piece of cake.

What if things aren’t this simple?

Sometimes, you need to think more deeply about things before you can write them down. Here’s an example: “Ron is building a trail to surround his rectangular garden. The dimension of his garden without the trail is 10×12. The total area of the garden with the trail around it should be 216 squared meters. How wide should he make his trial?”

This sounds difficult… but it isn’t. First thing you do is define your variables. Let t be the width of the trail. We know that we have t on each side of the original dimensions of the garden, so the total dimensions are (10+2t)x(12+2t). We also know that the total area is 216, so we can write an equation: (10+2t)(12+2t)=216. If you didn’t get any of that, draw a picture, it usually helps. Once you’ve got the equation down, note that this is a simple quadratic you can expand, simplify and solve easily.

What if I get crazy results?

Sometimes, modeling equations after real-life problems can get you some weird solutions. Say, for example, you tried solving a problem similar to the one above and got a nasty solution. What does that mean?

Irrational solutions indicate that the numbers don’t work out nicely. They’re not too bad though, all you have to do is convert the irrational into an approximated decimal, to as many decimal places as you want, and your answer should be good enough.

Imaginary solutions usually mean you got your numbers wrong, or you’re attempting to do something impossible. These are annoying and not fun to get, but if you work your way back up you can discover your error quickly most times.

Negative solutions don’t make much sense at times. In our earlier example, if you wanted the total area of the garden with the trail to be less than the area of the garden alone, you’ll get a negative solution. In real-life, there are no negative distances or measurements, so make sure the answer sign fits your question.

And now you should be able to practice lots of word problems, and use algebra to solve some every-day problems involving numbers, measurements and such. Don’t be afraid, math is your friend.

And for more help, check out the Algebra Problems Go-Through lessons.

Thanks for reading this Welcome to Algebra Lesson!

sweety2000
  • Authority 84
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sweety2000 said:

its amaaaaaaaaaaazin seriously

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  • Posted 5 months ago.
DK Arya
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DK Arya said:

so nicely said.

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  • Posted 5 months ago.
DIGITIMA
  • Authority 20
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DIGITIMA said:

Pardon my ignorance – can you let me know what is the value of t obtained in your case example?

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  • Posted about 10 hours ago.
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