# Problem Solving With Algebra

So let's draw this garden here, Tina's garden. But they also tell us that the actual numerical value of the perimeter is 60 feet. So this perimeter 6w must be equal to 60 if we assume that we're dealing with feet. We can divide both sides of this equation by 6 so that we have just a w on the left-hand side. We introduce students to the rich field of complex numbers, as well as to important common functions and concepts in discrete math.

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The problem is asking for both the numbers, so we can make “$$n$$” the smaller number, and “$$18-n$$” the larger.

$$\begin2n-3\,\,\,=\,\,18-n\\\underline\\3n\,-3\,\,=\,\,\,18\\\underline\\\,\,3n\,\,\,\,\,\,\,\,\,\,=\,\,\,21\\\,\frac\,\,\,\,\,\,\,\,\,\,\,=\,\,\frac\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,n=7\,\,\,\,\,\,\text\\\,\,\,18-7=11\,\,\,\,\text\end$$ Solution: We always have to define a variable, and we can look at what they are asking.

Note that Using Systems to Solve Algebra Word Problems can be found here in the Systems of Linear Equations and Word Problems section.

Now that you can do these difficult algebra problems, you can trick your friends by doing some fancy word problems; these are a lot of fun.

In Algebra 1, students learn how to work with various types of expressions both algebraically and geometrically.

They learn how to solve linear and quadratic equations and how to represent various expressions in the Cartesian plane.The problems here only involve one variable; later we’ll work on some that involve more than one.Doing word problems is almost like learning a new language like Spanish or French; you can basically translate word-for-word from English to Math, and here are some translations: Note that most of these word problems can also be solved with Algebraic Linear Systems, here in the Systems of Linear Equations section.We can just put a negative sign in front of the variable.If you’re not sure if you should multiply, add, or subtract, try “real numbers” to see what you should do.Now let’s do some problems that use some of the translations above.We’ll get to more difficult algebra word problems later. Solution: We always have to define a variable, and we can look at what they are asking.The problem is asking for a number, so let’s make that $$n$$.Now let’s try to translate word-for-word, and remember that the “opposite” of a number just means to make it negative if it’s positive or positive if it’s negative.The perimeter of Tina's rectangular garden is 60 feet. So if this is w, then the length is going to be 2w. If the length of the garden is twice the width, what are the dimensions of the garden?

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