# Problem Solving In Algebra

We can just put a negative sign in front of the variable.

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.

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 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.

For example, “ $$\displaystyle \begin\left( \right)n-3=2\left( \right)-33\\,\,\,\,\,-7n-3=-2n-33\\,\,\,\,\,\,\underline\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-3\,=\,\,\,5n-33\\,\,\,\,\,\,\,\,\,\,\,\,\,\underline\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,30\,\,=\,\,\,5n\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac\,\,=\,\,\frac\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,n=6\end$$ $$\displaystyle \beginx=20 \left( \right)\x=20 \left( \right)\x=20 3=23\x=23\,\end$$ or $$\displaystyle \beginx=20\times \left( \right)\x=20\times \left( \right)\x=20\times \left( \right)\x=23\,\end$$ Solution: This problem seems easy, but you have to think about what the problem is asking.

When we are asked to relate something to something else, typically we use the last thing (the “to the” part) as the $$y$$, or the dependent variable.

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.