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?

Question

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?

anonymous · Answer

First we need to find the slope so we need to write this info as 2 points. Which variable, s or t, would be the dependent variable?

anonymous · Answer

T?

anonymous · Answer

Nope, it would be s. In other words the weight of the strawberries produced depends on the time

anonymous · Answer

Actually S since it depends on the weight...right?

anonymous · Answer

S depends on the value of t. so s would be your 'y' and t would be your 'x' in (x,y)

anonymous · Answer

@CalebBeavers could you please help me on my question!?

anonymous · Answer

Okay, so what do we do now that we know that?

anonymous · Answer

Make two points with the info given. They would be (9/2, 1445) and (7, 2320)

anonymous · Answer

Now find the slope of those two points

anonymous · Answer

-2.5/875

anonymous · Answer

*2.5

anonymous · Answer

So it that the amount for one hour?

anonymous · Answer

*is

anonymous · Answer

you got the top and bottom mixed up, it should be 875/2.5 which is 350

anonymous · Answer

Ohh

anonymous · Answer

so now that we have a slope we can put this into point slope form and simplify it which will give us y=mx+b

anonymous · Answer

Have you ever done point slope form?

anonymous · Answer

Yea, but I basically suck at it

anonymous · Answer

Ha thats alright, ill walk you through it. the formula is $$y-y _{1}=m(x-x _{1})$$

anonymous · Answer

Where m is the slope, and (x1, y1) is whichever point you wanna use

anonymous · Answer

So which one?

anonymous · Answer

7 I guess lol

anonymous · Answer

Alright, (7, 2320). when we plug that and the slope in we get:
y-2320=350(x-7)

anonymous · Answer

Distribute the 350 and what do you get?

anonymous · Answer

We're dividing 350 by both sides?

anonymous · Answer

no distribute it into the parentheses

anonymous · Answer

<~< No clue how to do that (just started learning this today so bare with me)

anonymous · Answer

Where you multiply 350 times everything in the parentheses, so you'd get:
y-2320=350x-2450

anonymous · Answer

ohhh I feel dumb lol

anonymous · Answer

haha its alright, now that weve done that, add the 2320 to both sides

anonymous · Answer

2320y=350x-130. right? (otherwise I'm guessing 2320y=2670x-130)

anonymous · Answer

You should only be left with y on the left, when you add 2320 it gets rid of it on the left and then you just add it to the last number on the right

anonymous · Answer

x.x oops

anonymous · Answer

Soo, it's actually y=350x-130?

anonymous · Answer

yep. And since we said s is the y variable and t is the x variable, lets go ahead and change those. so we have:

s=350t-130

so if you wanna find how many pounds you can produce in 11 hours, what would you do?

anonymous · Answer

You would substitute and get s=350(11)-130 or y=3720

anonymous · Answer

Yep so you can produce 3720 pounds in 11 hours

anonymous · Answer

Wow that's super easy actually , thanks so much!

anonymous · Answer

You're welcome