SIMPLE WORD PROBLEMS RESULTING IN LINEAR EQUATIONS
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Many word problems, upon translation, result in two equations involving two variables (two ‘unknowns’).
In mathematics, a collection of more than one equation being studied together is called a system of equations.

This section can be included in a high-level Algebra I curriculum.
It is also available in the Algebra II curriculum, where systems are studied in much more detail.

The systems in this section are fairly simple, and can be solved by substituting information from one equation into the other.
The procedure is illustrated in the following example:

Antonio loves to go to the movies. He goes both at night and during the day. The cost of a matinee is \$6.00. The cost of an evening show is \$8.00. If Antonio went to see a total of [beautiful math coming... please be patient] $\,12\,$ movies and spent \$86.00, how many night movies did he attend?

THE GOOD NEWS!

Even though this explanation was very long, you'll actually be writing down very little!
Here's the word problem again, and what I ask my students to write down:

Antonio loves to go to the movies. He goes both at night and during the day. The cost of a matinee is \$6.00. The cost of an evening show is \$8.00. If Antonio went to see a total of $\,12\,$ movies and spent \$86.00, how many night movies did he attend?

Let [beautiful math coming... please be patient] $\,n = \text{# night tickets}\,$.
Let [beautiful math coming... please be patient] $\,d = \text{# day tickets}\,$.
[beautiful math coming... please be patient] $n + d = 12$
[beautiful math coming... please be patient] $8n + 6d = 86$
[beautiful math coming... please be patient] $n = 12 - d$
[beautiful math coming... please be patient] $8(12-d) + 6d = 86$
[beautiful math coming... please be patient] $96 - 8d + 6d = 86$
[beautiful math coming... please be patient] $96 - 2d = 86$
[beautiful math coming... please be patient] $-2d = -10$
[beautiful math coming... please be patient] $d = 5$   (circle this)
[beautiful math coming... please be patient] $n + 5 = 12$
[beautiful math coming... please be patient] $n = 7$  (circle this)
[beautiful math coming... please be patient] $7 + 5 \,\,\overset{\text{?}}{=}\,\,12$  
[beautiful math coming... please be patient] $8(7) + 6(5) \,\,\overset{\text{?}}{=}\,\,86$  

Antonio attended  7  night movies.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Solving Simple Linear Inequalities with Integer Coefficients

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
(MAX is 7; there are 7 different problem types.)