Question

So here is the informatiovn: A delivery serice charges a base price for an overnight delivery of a package plus an extra charge for each pound the package weighs. A customer is billed $22.85 for shipping a 3-pound package and $40 for shipping a 10-pound package. Now the question is to write an equation that gives the total cost of shipping a package as a function of the weight of the package. I am stuck on this and have no idea how to solve it. Can someone please give me an answer? AND FAST!

Answer 1

price = base price + per pound rate * weight
right?

Answer 2

Yes

Answer 3

okay, let's the base price B, and the per pound rate P

then the price to ship a package that weighs x pounds is
C = B + Px

now, we know two different package weights and their prices.

3 pounds for $22.85
10 pounds for $40

we can make two equations from that data:

22.85 = B + P(3)
40 = B + P(10)

can you solve that system of equations for B and P?

Answer 4

Yes hold on.

Answer 5

For 22.85 = B + P(3) I got B=P3+22.85. Am I right so far?

Answer 6

if you have

22.85 = B + 3*P and you want B all alone, you can subtract 3*P from both sides:

22.85 - 3*P = B + 3*P - 3*P
22.85 - 3*P = B

Answer 7

do you know about slope intercept form for a line equation?

Answer 8

Yes.

Answer 9

do the equations we've written remind you at all of that?

Answer 10

Yes.

Answer 11

good! it's exactly the same. in fact, we could solve this problem by making a plot of those two points, drawing a line through them, and seeing where the line crosses the y-axis. that would give us the base price, and the slope of the line is the price per pound.

Answer 12

but let's continue with the approach you were trying. You got

B = 22.85-3*P

Now substitute that into the other equation:

40 = B + 10*P
40 = 22.85-3*P + 10*P
solve that for P

Answer 13

I got 17.15=P

Answer 14

Am I right?

Answer 15

????????

Answer 16

hmm, not quite right.

40=22.85 - 3*P + 10*P

40 = 22.85 + 7P
right?

Answer 17

sorry, thought I clicked the Post button, but apparently OS didn't think so :-)

Answer 18

Oh I made a simple mistake, but I understand now.

Answer 19

And also a whole bunch of other mistakes.LOL

Answer 20

so what do you get for the value of P? and from that, with the substitution equation, what is the value of B?

Answer 21

Ok, so I got P=2.45.

Answer 22

yes!

Answer 23

YAY

Answer 24

so $2.45 per pound. how much is the base price?

Answer 25

One second...

Answer 26

the cost of shipping a weightless package, if you want to think of it that way :-)

Answer 27

OK B=15.5?

Answer 28

yep, you nailed it!

Answer 29

should check the work, of course:

3 pound package:
C = 15.5 + 3*2.45 = 15.5 + 7.35 = 22.85

10 pound package
C = 15.5 + 10*2.45 = 15.5 + 24.50 = 40

looks good!

Answer 30

K

Answer 31

Here's a graph

Answer 32

So would that answer the question?

Answer 33

(the equation that is)

Answer 34

Yes, C = 15.5 + 2.45w

if C is the cost and w is the weight

Answer 35

Thank you, but I have a question about another question.
How can you tell if data can be modeled by a linear equation?

Answer 36

well, if you plot the data and it is pretty much a straight line, then a linear equation will model it. Or, even if it isn't a straight line, if the area of interest is small enough, a straight line may model the area of interest adequately.

Answer 37

I have to write an equation in point-slope form that relates y to x. Can you help me with that?

Answer 38

sure, but you can do it yourself now. just do the same thing we did for the shipping problem!

Answer 39

Oh ok.

Answer 40

give it a try, I'll answer your questions if you get stuck

Answer 41

I actually have to get off the computer now, but thank you for your help!

Answer 42

Your welcome!!

Answer 43

tag me in the future if you need help — just put "@whpalmer4" in a post and I'll get a notification. I'll try to help you when I'm next online.

Answer 44

Ok I`ll be sure to.