Download Modeling equations:

Modeling equations:
We’ve discussed using equations to model real problems and situations by setting up a
variable for the unknown. Consider the following example that we’ve worked previously
in our homework:
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22.
Value Rent-A-Car rents vans at a daily rate of $84.95 plus 60 cents per mile.
Molly rents a van to deliver electrical parts to her customers. She is allotted a
daily budget of $320. How many miles can she drive for $320?
One method of solution is to focus on the unknown. If we let x = the miles driven
by Molly, we can say that renting a van for “60 cents per mile” is equivalent to
0.60x, and we can set up the following equation to represent the cost to Molly:
84.95 + 0.60x = 320
We can then solve by subtracting 84.95 from both sides of the equation and then
dividing both sides by 0.60 to get 391.75 miles. Check this number to confirm
that it is the solution to the problem.
Consider the next problem which also requires you to model in the form of an equation:
The price of a TV set from the company PanaSony varies according to how many
are available. The TVs start at $340 and go down $1.30 in price for each one
available (this will only continue until 200 are available, because if this were to
continue, eventually the TVs would be free for all people!)
a.
What does the cost of the TVs depend on? Using the variable “x” to
represent this unknown, write a formula for the cost of a TV.
b.
Use your information from part a to answer the questions:
o How much will a TV cost if 1 is made available?
o How much will a TV cost if 2 are made available?
o How much will a TV cost if 3 are made available?
o How much will a TV cost if 10 are made available?
o How much will a TV cost if 200 are made available?
c.
Assume that an appliance store wants to buy TVs from PanaSony to sell
on their own. How much total money will they pay if:
o Purchase 1 TV?
o Purchase 2 TVs?
o Purchase 3 TVs?
o Purchase 10 TVs?
o Can you write a general formula for the total price the appliance store
of the TV’s if they purchase x number of TV’s?
d.
Now for the possibly more challenging question!!! How many TV’s can
they purchase with $10,000? See if you can figure this out. Maybe you
can use guess and check, maybe you can use algebra.