# Equation Problem Solving

A wording such as "an equation in x and y", or "solve for x and y", implies that the unknowns are as indicated: in these cases x and y. Note that the set of solutions can be the empty set (there are no solutions), a singleton (there is exactly one solution), finite, or infinite (there are infinitely many solutions).For example, an equation such as One particular solution is x = 0, y = 0, z = 0.As a reminder, a is just an algebraic expression that represents a line.

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In these equations, we're trying to figure out the variable, which involves getting it alone on one side of the equals sign.

There are simple problems that involve linear equations.

Well, I like trains, but I still feel a little nervous when I read a math problem that starts with a train. Our variable here is the amount of interest, so let's call that x. Your cell phone company is promoting a text message plan that costs \$10 each month plus five cents per text.

If I'm going to have to translate a real world scenario to an algebraic equation, can't it be something I might actually encounter in my life? The interest will be the amount of the loan, \$500, multiplied by the interest rate, 4%. You currently pay \$20 each month for an unlimited plan, but you want to save a few dollars.

I mean, I've ridden trains between Chicago and New York, but I've never plotted when my train will pass another. To multiply with a percent, we convert it to a decimal. If you want to try the new plan and spend only \$15 each month, how many texts can you send?

In this lesson, we'll not only practice solving problems that can be translated into linear equations, we'll also focus on problems you may encounter in your life - problems not involving trains passing each other. If we solve for x by subtracting 35 from both sides, we get x = 37. They can be a bit more complex, like this: 15 less than four times a number is 57.

The second train is going 85 mph for t time, or 85t. In other words, when do the two distances add up to the total distance, 800 miles. Now, we divide both sides by 160, and we get t = 5.

The first train is traveling at a rate of 75 mph, so the distance it covers in t time is 75t.

Try it risk-free From sale prices to trip distances, many real life problems can be solved using linear equations. Let's say you're a little short on cash and need a loan. You've been averaging way more than that, so maybe this isn't a great plan. If you can save each week, how many weeks will it take you to get the bike? We focused on defining the variable, or the unknown quantity, in terms of what is known, then solving for the variable.

In this lesson, we'll practice translating word problems into linear equations, then solving the problems. Let's take that knowledge and look at some real life situations. Your cousin agrees to loan you money, and you agree that you'll repay him in full plus 4% interest. But, then you get a new job, and suddenly you have some extra cash. Oh, and we solved the dreaded algebra train problem. You'll be able to translate word problems into linear equations and solve those equations after watching this video lesson. We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities.

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