Question

The Sugar Sweet Company is going to transport its sugar to market. It will cost
$4500
to rent trucks, and it will cost an additional
$125
for each ton of sugar transported.
Let
C
represent the total cost (in dollars), and let
S
represent the amount of sugar (in tons) transported. Write an equation relating
C
to
S
. Then use this equation to find the total cost to transport
13
tons of sugar.

Answer 1

@TheSmartOne

Answer 2

Can you make the equation in the form of y = mx + b?

b is the y-intercept, m is the slope

They said it costs 4500 to rent trucks. It doesn't matter whether they put nothing on that truck or sugar on that truck. They will still have to pay a one time fee of 4500.

The 125 fee is per each ton of sugar

Answer 3

So would 4500 + 125 = y?

Answer 4

you're forgetting about tons of sugar

we don't know how many tons of sugar we'll have so we have to have a variable for that

it can be x or it could be S like the question wants

and you can replace y with C so that way it's the equation the question wants :)

Answer 5

The tons of sugar it's asking is 13. So would the equation be C=13s+125

Answer 6

That's the question. We're trying to find the equation first.

An example:
It will cost me 5 dollars to open my shop. It costs me 2 dollars to make each cookie. Write an equation for the total cost for selling x cookies.

5 dollars is a one time fee. I have to pay it regardless of how many cookies I make.
I make a cookie for 2 dollars. Each cookie I sell gets me 2 more dollars.

The equation, where y is total cost and x is number of cookies made is
y = 2x + 5

and then there's this next question that asks how much does it cost to make 10 cookies. You then plug in 10 in place of x and solve for y

y = 2(10) + 5
y = 20 + 5
y = 25

It costs me 25 dollars to make 10 cookies


so apply this example to your question :)

Answer 7

y=4500(13)+125?

Answer 8

or y=4500+125(13) since it said add 125 for each ton of sugar.

Answer 9

yes, the second equation you wrote is correct :)

Answer 10

Omg thank you so much. My brain is a little blah from working on math for so many hours. Thanks again!

Answer 11

just make sure to solve for y :)

unless the answer choices left it like that

Anytime! :D

Answer 12

For y I got 6125.

Answer 13

Correct :)

Answer 14

This is a classic problem requiring the use of the slope-intercept form of the equation of a straight line. You are given a fixed cost, $4,500, which is your y-intercept; you are given a unit cost, the cost of transportation for each ton of sugar.

$4,500 is already in the correct units of measurement: dollars. The variable costs will be in dollars also, if you multiply the cost per ton transported by the number of tons transported.

Try hard to recognize that this whole problem is based on the equation y=mx+b, which you have likely seen before.

Answer 15

Again: b=the y-intercept=the upfront cost of renting the trucks=$4,500

m=the charge per ton of sugar transported = $125/ton
x= the number of tons of sugar transported

If you multiply ($125/ton) by (x tons), that comes out to $125x dollars, which is the correct unit of measurement in this case.