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Solving Two-step Equations - Problem 3

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Word problems can be solved by setting up an equation and solving for the unknown variable. Start by translating the word problem and writing it as a mathematical sentence, using a variable for the unknown value. Next, solve the equation using inverse operations to isolate the variable. Remember that solving an equation and finding the value of the variable requires "undoing" what has been done to the variable. Since an equation is two expressions that are equal to each other, this means that what is done to one side of the equation has to be done to the other side as well so that the equation stays balanced. In a two-step equation, work in the reverse order of PEMDAS.

This is the kind of problem that strikes fear into every student's heart so I want you guys to take a deep breath and know that we can do the word problems. Okay a total bill for 3 hats and $2.50 tax is $44.50. How much does each hat cost?

There's a couple different ways to do this. One way you guys might have learned in your previous Math courses is to make a guess and check chart and just kind of like plug in values and see how that goes. The great thing about Algebra though is that you can get it correct the first time. It's like a shortcut when you can do an equation. Let me show you how this could work. Okay the total bill for 3 hats and 2.50 tax, I'm going to write that like this, 3 hats, h for hats and then I also have to pay 2.50 tax and I know that the total bill is $44.50. I have all my numbers accounted for. I'm accounting for those 3 hats plus the $2.50 tax.

This is an equation that when I solve for h, I'm going to know how much each hat costs so it's pretty cool. So let's see. In order to get h by itself I need to undo all this business so I'll subtract 2.50 from both sides, that's the opposite of adding so I'll have 3h, that's all that's left on that side, is going to be equal to $42 right? $41, $42, yeah. So now I know that 3 hats cost $42, the last thing I want to do is divide both sides by 3 to find out that each hat is equal to whatever 42/3 is. If you're not sure go ahead and do out this long division where I find out that they are $14 per each hat.

Also make sure that you put units on your answer, units meaning the dollar sign. It's not like h equals 14, you have to specify each hat costs $14. In fact it would be A plus to say like hat equals $14, something like that so you remind yourself that this is not just some plain old letter, h stands for how much each hat costs. Again you guys when you have a word problem you could try guessing checking but that takes a long time. If you can turn it into an Algebra equation it will go much, much faster.

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