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) About Me  (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 (10,15) and (30,40)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (10,15) and (x%5B2%5D,y%5B2%5D) is the second point (30,40))


m=%2840-15%29%2F%2830-10%29 Plug in y%5B2%5D=40,y%5B1%5D=15,x%5B2%5D=30,x%5B1%5D=10 (these are the coordinates of given points)


m=+25%2F20 Subtract the terms in the numerator 40-15 to get 25. Subtract the terms in the denominator 30-10 to get 20




m=5%2F4 Reduce



So the slope is

m=5%2F4





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




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


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


y-15=%285%2F4%29%28x-10%29 Plug in m=5%2F4, x%5B1%5D=10, and y%5B1%5D=15 (these values are given)



y-15=%285%2F4%29x%2B%285%2F4%29%28-10%29 Distribute 5%2F4


y-15=%285%2F4%29x-25%2F2 Multiply 5%2F4 and -10 to get -50%2F4. Now reduce -50%2F4 to get -25%2F2

y=%285%2F4%29x-25%2F2%2B15 Add 15 to both sides to isolate y


y=%285%2F4%29x%2B5%2F2 Combine like terms -25%2F2 and 15 to get 5%2F2 (note: if you need help with combining fractions, check out this solver)



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

Answer:



So the equation of the line which goes through the points (10,15) and (30,40) is:y=%285%2F4%29x%2B5%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=5%2F4 and the y-intercept is b=5%2F2


Notice if we graph the equation y=%285%2F4%29x%2B5%2F2 and plot the points (10,15) and (30,40), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%285%2F4%29x%2B5%2F2 through the points (10,15) and (30,40)


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) graph%28500%2C500%2C-20%2C140%2C-20%2C140%2C%285x%2F4%29%2B%285%2F2%29%29
.
Ed

Answer by ankor@dixie-net.com(22740) About Me  (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 = %28y2-y1%29%2F%28x2-x1%29
Using the given data assign as follows:
x1=10, y1=15; x2=30, y2= 40
:
m = %2840-15%29%2F%2830-10%29 = 25%2F10 = 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
:
+graph%28+300%2C+200%2C+-10%2C+110%2C+-10%2C+140%2C+1.25x%2B2.5%29+
:
How about this, you got a handle this now?