Question 1199003
.
Ben's monthly phone bill includes a fixed charge, which is the same each month, 
and an additional flat rate charge for each long distance call. 
One month the bill was $32, which included charges for 4 long distance calls. 
The following month the bill was $38, which included charges for 6 long distance calls. 
Find the fixed charge and the additional flat-rate charge per long distance call. 
Assign variables and write the equations
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<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part 1</H3>

<pre>
First, everything can be solved without any equations.


The difference between the two monthly bills is 38-32 = 6 dollars and 6-4 = 2 calls.


Hense, each call cocts 6/2 = 3 dollars.


Then the fixed monthly charge is  32 - 4*3 = 20 dollars (using the data of the 1st month).


So, the problem is just solved in this way.
</pre>

<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part 2</H3>

<pre>
With equations, let "a" be the fixed monthly charge and let "b" is the rate per one call.


Then the monthly cost equation is 

    C = a + bx.

where x is the number of calls.


You write it for two consecutive months

    a + 4b = 32,    (1)

    a + 6b = 38.    (2)


Then you subtract equation (1) from equation (2)

        6b - 4b = 38 - 32

           2b   =    6

            b   =    6/2 = 3.    Thus, in this part, you simply REPEAT
                                 operations, which I did mentally in the first part.


Having  b= 3,  you find "a" from equation (1) as

    a = 32 - 4*3 = 20.           Exactly as I did it in my first solution.
</pre>

Solved, with full explanations.


The lesson to learn from this my lecture is that this problem can be solved mentally
in couple of seconds without using any equations.



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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/HOW-TO-solve-these-simple-word-problems-MENTALLY-without-using-equations.lesson>HOW TO solve these simple word problems MENTALLY without using equations</A> 

in this site.


Read it and get be trained in &nbsp;MENTAL &nbsp;solution of similar problems.