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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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Part 1
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.
Part 2
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.
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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To see many other solved similar and different problems, look into the lesson
- HOW TO solve these simple word problems MENTALLY without using equations
in this site.
Read it and get be trained in MENTAL solution of similar problems.