SOLUTION: I am helping my daughter with her homework and have no idea what I am doing. Computer diskette problem: A computer store sells 10 floppy diskettes for $15, and 30 for $40. Ass

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Question 109178: I am helping my daughter with her homework and have no idea what I am doing.
Computer diskette problem: A computer store sells 10 floppy diskettes for $15, and 30 for $40. Assume that the number of dollars varies linearly with the number of diskettes.
a) Write the particular equation expressing dollars in terms of diskettes.
b) Predicit the price for a box of 100.
c) State the domain for your variable.
d) Sketch and label the graph.
Found 2 solutions by edjones, ankor@dixie-net.com:
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
a) Let x=number of disks, y=price of the disks.
Plot 2 points.
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (,) and (,)


Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))


Plug in ,,, (these are the coordinates of given points)


Subtract the terms in the numerator to get . Subtract the terms in the denominator to get




Reduce



So the slope is







------------------------------------------------


Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
where is the slope, and (,) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


Plug in , , and (these values are given)



Distribute


Multiply and to get . Now reduce to get

Add to both sides to isolate y


Combine like terms and to get (note: if you need help with combining fractions, check out this solver)



------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (,) and (,) is:


The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is


Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver)


Graph of through the points (,) and (,)


Notice how the two points lie on the line. This graphically verifies our answer.



.
b) 5*100/4+ 5/2
=500/4+ 5/2
=125+2.5=$127.50 for box of 100
.
c) domain is all real integers greater than 0.
.
d)
.
Ed

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
A computer store sells 10 floppy diskettes for $15, and 30 for $40. Assume that the number of dollars varies linearly with the number of diskettes.
:
a) Write the particular equation expressing dollars in terms of diskettes.
:
Let x = no. of floppies sold
Let y = cost of the item
:
find the slope of the equation, slope formula: m =
Using the given data assign as follows:
x1=10, y1=15; x2=30, y2= 40
:
m = = = 1.25 is the slope
:
Find equation using the point/slope formula: y - y1 = m(x - x1)
:
y - 15 - 1.25(x - 10)
y - 15 = 1.25x - 12.5
y = 1.25x - 12.5 + 15
y = 1.25x + 2.5; is the equation expressing cost in terms of no. of items
:
:
b) Predict the price for a box of 100.
:
Substitute 100 for x in the equation we just created:
y = 1.25(100) + 2.5
y = 125 + 2.5
y = $127.5 is the cost of 100 items
:
:
c) State the domain for your variable.
:
The domain would be all real integers => 1. You can't include 0 because in our
equation the cost of 0 items is $2.50, hardly reasonable.
:
d) Sketch and label the graph.
You can plot the points given and draw a straight line thru them, it should look like this:
y (vertical is cost) and x (horizontal) is no. of items sold
:

:
How about this, you got a handle this now?
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