Question

HELP ME PLEASE MEDAL WILL BE GIVEN

Answer 1

what is the question

Answer 2

@zepdrix

Answer 3

wuts the prob bro

Answer 4

A cannery processed 1,445 pounds of strawberries in 4.5 hours. The cannery processed 2,320 pounds in 7 hours. Write a linear equation to model the relationship between the weight of strawberries S and time T. How many pounds of strawberries can be processed in 11 hours

Answer 5

@zepdrix

Answer 6

@funinabox

Answer 7

funina box is offline

Answer 8

Ok ok ok let's see here...

Answer 9

Like the previous problem we did, this one can also be represented by a `linear function`.

So we want to write something like this:\[\Large y=mx+b\]
Err oh wait, do you have multiple choice for this one?
Maybe we should look at those before we choose to jump into slope-intercept form.

Answer 10

no i dont but i am not doing a graph either

Answer 11

Ok let's just try it this way then :D

For our problem we'll instead want to write it this way,\[\Large T=mS+b\]We're using the coordinates (S,T) instead of (x,y) for this problem.
Try not to get too confused by that! :O

Answer 12

ok

Answer 13

i'll try wont be easy though lol

Answer 14

XD

Answer 15

From the information they gave us, we can write the relationships as ordered pairs.

\[\Large (S_1,\;T_1) \quad =\quad (1445,\;4.5)\]\[\Large (S_2,\;T_2) \quad=\quad (2320,\;7)\]

Answer 16

Remember how to find slope?? :D

Answer 17

yeah

Answer 18

It's gonna look a little weird since we're not using x and y.
Hopefully it looks familiar though.\[\Large m=\frac{T_2-T_1}{S_2-S_1}\]

Answer 19

So what do you get for your slope? :D

Answer 20

\[m=\frac{ 7-4.5 }{2320-1445 }\]

Answer 21

\[\frac{ 2.5 }{ 875 }\]

Answer 22

Ok looks good.
Let's multiply the top and bottom by 2, so we can get rid of the decimal.\[\Large m=\frac{5}{1750}\]

Answer 23

why would we do that it is not in the equation so it could mess the equation up

Answer 24

We didn't change the `value` of the fraction.
We just changed how it looks.

It's just easier to read now.

Answer 25

ok

Answer 26

we could do it as \[\frac{ 1 }{ 350 }\]

Answer 27

oh nice! lol

Answer 28

simplify it 2.5 goes into 875 evenly tada lol

Answer 29

\[\Large T=mS+b\qquad\to\qquad T=\frac{1}{350}S+b\]To find b, we simply plug in one of our ordered pairs and solve for it!

\[\Large 7=\frac{1}{350}(2320)+b\]

Answer 30

ok what next?

Answer 31

So what do you get for \(\Large b\) ? :D solve the equation!!

Answer 32

.371528

Answer 33

Yah, let's leave it as a fraction for right now I guess.

\[\Large b=\frac{130}{350} \qquad\to\qquad b=\frac{13}{35}\]

Answer 34

ok what next?

Answer 35

So we've successfully found a linear equation for our relationship.\[\Large T=mS+b \qquad\to\qquad T=\frac{1}{350}S+\frac{13}{35}\]

Answer 36

The next part of the question is asking us, when \(\Large T=11\), solve for \(\Large S\)

Answer 37

\[11=\frac{ 1 }{ 350 }S+\frac{ 13 }{ 35 }\]

Answer 38

@thomaster

Answer 39

@phi @jim_thompson5910 @ganeshie8