The most fundamental equations are linear equations, and every successful pre-algebra and algebra student becomes very proficient at solving them.   What can prove to be a bit more challenging is solving story problems modeled by linear equations.  The simple proportion is often one of the first type of application problems introduced.  Here is an example:

Emma is going to surprise her mother by making a chocolate custard dessert.  The recipe calls for 5 eggs and 1 cup of sugar.  When she goes to the refrigerator, she discovers that there are only 4 eggs!  How much sugar should she use to adjust the recipe?

Emma is in a bit of a predicament.   She writes down the following information and studies it for a few moments:

5 eggs  needs   1 cup of sugar
4 eggs  needs   x cups of sugar

Suddenly, she remembers a lesson on proportions from her algebra class!  She writes down 5 eggs/1 cup sugar is equal to 4 eggs/x  cups sugar.  After another pause, she recalls that "the product of the means equals the product of the extremes." Cross muliplying, she has

4 eggs * 1cup sugar  = 5 eggs * x  cups sugar

This is now the linear equation:
4*1=5*x

She then immediately proceeds to use the Division Postulate to divide both sides of the equation by 5 (or she could have used the Multiplicaton Postulate and multiplied both sides by 1/5).  She has the solution:
; she needs 4/5 cup of sugar

Later, when the custard is served to her delighted mother, it tastes delicious!!

While the following problem does not use a proportion, it is still a relatively simple linear equation in one variable.  See if you can help out Joe:

Joe has invited Natalie to dinner and a movie.  He has a total of $25 to spend on the date.  The movie tickets cost $4.50 apiece.  At dinner, Joe orders a soft drink for $1.50 and Natalie has a $1.25 coffee.  She then orders an entree that costs $5.75.  If the sales tax on the meal is 7 1/2 % and he plans to tip 15% after the tax has been added, what is the most expensive entree that Joe can order?