Problem Solving In Algebra

Problem Solving In Algebra-17
Solution: First we define a variable \(h\), which will be the number of hours that Erica must study (look at what the problem is asking).We know from above that “at least” can be translated to “\(\ge\)”.

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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 will see later that this is like a Slope that we’ll learn about in the Coordinate System and Graphing Lines including Inequalities section.

Here’s the math: To get the rate of minutes to photos, we can set up a proportion with the minutes on the top and the photos on the bottom, and then cross multiply.

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

Problem Solving In Algebra

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

So the equation relating the number of color photos \(p\) to the number of minutes \(m\) is \(\displaystyle m=\fracp\). Let’s see how we can set this up in an equation, though, so we can do the algebra!

There are actually a couple of different ways to do this type of problem.

Then \(10-J\) equals the number of pounds of the chocolate candy. This one is a little more difficult since we have to multiply across for the Total row, too, since we want a Don’t worry if you don’t totally get these; as you do more, they’ll get easier.

We’ll do more of these when we get to the Systems of Linear Equations and Word Problems topics.


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