You are comparing two cell phone plans. Company A offers a monthly fee of
thirty-five dollars plus ten dollars per gigabyte of data. Company B offers a
monthly fee of seventy dollars plus five dollars per gigabyte of data. Number one
write linear equations that model of the cell phone plans. Before we do this
we need to define variables to represent the unknowns. We have two unknowns.
We don't know the monthly cost or the number of gigabytes use per month.
Let's let C equal the monthly cost and X equal the number of gigabytes of data
used per month.
Now that we've defined the variables, we can write the linear equations that
model the two cell phone plans. fFor company A, the monthly cost C is equal to
thirty five dollars plus ten dollars per gigabyte of data.
Therefore we have C equals 35 plus 10x. For company B the monthly cost C
is equal to seventy dollars plus five dollars per gigabyte of data. Therefore we
have C equals 70 plus 5x. For number 2 if 4 gigabytes of data is used each month
which company is cheaper and by how much?
If 4 gigabytes of data is used we know x equals 4. To answer this question we
substitute 4 for X in both cost equations. For company A, the monthly cost C
is equal to 35 + 10 times 4, which equals 35 + 40, which equals 75.
Of course the units are dollars so if 4 gigabytes of data is used per month
company A will charge seventy-five dollars per month
Now for company B, the month cost C is equal to 70 plus 5 times 4, which is 70 +
20, which equals ninety dollars. So if 4 gigabytes of data is used each month,
company B will charge ninety dollars per month. So we know company A is cheaper. To
determine how much cheaper, we find the difference of these two amounts. 90 - 75
is equal to 15.
Therefore company A is cheaper by fifteen dollars per month.
Number three, if 12 gigabytes of data is used each month which company is
cheaper and by how much? Same type of question but now we're given x equals 12.
For company A, the monthly cost C is equal to 35 + 10 x 12 which equals 35 + 120,
which equals 155 dollars per month as a monthly cost. Company B, the monthly cost C
is equal to 70 + 5 x 12, which equals seventy plus 5 times 12 is 60, 70 plus 60
equals 130. Again the units are dollars so if 12 gigabytes of data is used each
month, notice now
Company B is cheaper by twenty-five dollars per month.
We know it's $25 because 155 minus 130 equals to 25. Company
B is cheaper by twenty-five dollars per month.
Now for the last question, how many gigabytes per month would yield equal
monthly statements from both companies,
what would the monthly cost be? Let's answer this question on the next slide. To
determine how many gigabytes per month will yield equal monthly payments we will
determine when the cost will be the same and this occurs when 35 + 10x is equal
to 70 + 5x. 35 + 10 x equals the monthly cost the company A and seventy plus 5x
equals the monthly cost for a company B. If we solve this equation for x we can
determine
how many gigabtyes per month would yield equal monthly statements. To solve for
x we need to have the X terms on one side of the equation. Let's subtract 5X
on both sides.
Simplifying we have 35, 10x minus 5x is 5x, so we have plus 5x equals seventy
and 5x minus 5x is equal to 0.Now we isolate the X term on one side of
the equation by subtracting 35 on both sides.
Simplifying, 35 - 35 is zero giving us 5x equals 70 - 35 is equal to 35.
The last step to solve for x, we divide both sides by 5.
Simplifying 5/5 simplifies to 1. 1 times x is x. x equals 35 divided by 5, which
equals seven.
Now we can answer the first question. The monthly cost is the same for both
companies if seven gigabytes of data is used per month.
Now to answer the question what will the monthly cost be. We substitute x into
either equation because remember this is when the cost of companies will be the
same.
Let's just go ahead and use this first equation. Here monthly cost C is equal to
35 + 10 times 7, which equals 35 + 70, which equals 105 dollars per month.
Let's verify that we also get 105 if we substitute 7 into the second equation.
We would have C equals 70 plus 5 times 7. 70 + 35 which is equal 105.
Now we know the cost would be 105 dollars per month.
Before we go let's also look at this graphically. If you were to graph these
two equations on the coordinate plane where we have a number of gigabytes per
month on the horizontal axis and the cost per month in dollars on the
vertical axis, notice how these two lines intersect at this point here. The coordinates
of this point are 7 comma 105. The seven represents the number of gigabytes where the
two plans have the same cost. The 105 represents the monthly cost for both plans.
I hope you found this helpful.