Algebra Problem?

Question

A computer store sells 10 floppy diskettes for 15 dollars and 30 disks for 40 dollars. The dollars varies linarly with the disks. Predict the price for a box of 100 disks.

I got 157 dollars, and y = mx + b, I got 32 as my b, I think something is wrong here =(

Please help >_<

Answer 1

Let x be the number of disks and y the cost
slope = m = (40 - 15)/(30 - 10) = 25/20 = 1.25

So: y = 1.25 x + b

Now find b by using the first point (10 discs for 15 dollars):
15 = 1.25(10) + b
b = 2.50

y = 1.25x + 2.50
Check using the other point: 40 = 1.25(30) + 2.50 = 40 so OK.

For 100 disks, put this value in for x:
y = 1.25(100) + 2.50
y = 127.50

So the cost of 100 disks is 127.50

Answer 2

Let x = price difference between 40 and 100 units.
Ratio:
Unit diff:Price diff = Unit diff: Price diff
(30 - 10) : (40 - 15) = (100 - 40) : x
20 : 25 = 60 : x

20x = 1,500
x = 75

Solution: Price difference + cost of 40 units
75 + 40 = 115

Answer: The probable price of 100 disks is $115.

Answer 3

From the information given, an additional 20 disks sell for an additional 25 dollars, so each disk sells for $1.25. As a result, an additional 70 disks would sell for an additional $87.50, meaning the predicted price should be $40 + 87.50, or $127.50.

Answer 4

First find the slope
x= discs y=money
(40-15)/(30-10)
25/20
5/4

then plug in to create your equation
(y-15)=5/4(x-10)
y-15=5/4x-50/4
y=5/4x+2.5

Plug in 100 for x
y=5/4(100)+2.5
y=$127.50

Seems outrageous, but that's ok!!

Answer 5

this is a function of how the discount increase

10 @ 1.5 30 @ 1.333333

1.5-1.33333 = 0.16666666
this discount rate looks to me

Changes in cost per unit 0.16666 over number 20

cost for 100 $ 83.33 is it a deal ?