Question

I honestly don't understand how to solve linear word problems... Can someone help me solve one?

Answer 1

I honestly don't understand how to solve linear word problems..

Here's the quesion:

1a. ) The Peanut gallery made a profit of $16,450 in 2002, and a profit of $21,340 in 2005. Assume that the profit followed a linear pattern. Write an equation that gives the profit, y, in terms of the year, x. Let x=0 correspond to 2000.

Equation:

1b.) What was the profit in 2008

1c.) In what year would the profit be $31, 120 in the trend continued?

Please show explanations & work. I really..don't understand this.

(I obviously know the basics- solving equations, finding slope from an equation, y=mx + b, etc.)

Answer 2

ok, so you know the generic linear equation y=mx+b,
and you also know that y=profit, x = year (where x=0 corresponds to year 2000),
also, you are given enough data to set up two linear equation of the form y=mx+b.
can you try to set up two equations?

Answer 3

if you need farther help, ask :D

Answer 4

Um..I don't know..

Answer 5

You're supposed to find one equation of this problem. That can be done, by using more than one equations I think..

Answer 6

alright, so in the year 2002 (x=2), the profit is y = 16450, then that means:
A: 16450 = 2m + b

can you set up equation B?

Answer 7

Equation "B" as in finding the slope?

Answer 8

i mean another linear equation which i denote as "B", similar to equation "A" that I've set up above

Answer 9

Okay. I need clarification. My Algebra teacher solved this problem like this:

Answer 10

Can you explain what she (teacher) did there?

Answer 11

the equation is correct.
what your teacher did is solve a system of two linear equations, which are the equations A which as shown earlier, and equation B, which has a very similar setup as A.

to match what your teacher did, let A and B be two linear equations as shown below:
A: y = mx + b
B: Y = mX + b
then, to solve for m:
m = (Y-y)/(X-x)

Answer 12

after solving for m, plug m back into either A or B to solve for b, and you get your equation :D

Answer 13

What is equation "A" & "B"?

Answer 14

equation "A" was shown earlier, remember? and "B" has a similar set up using the data given

Answer 15

"alright, so in the year 2002 (x=2), the profit is y = 16450, then that means:
A: 16450 = 2m + b

can you set up equation B?"

Answer 16

Oh. Yeah. Of course. Could you solve 1b for me?

Answer 17

i can help you on 1b, but can you show me your 1a first :D

Answer 18

Okay. y = 1630(2002) +13190

Answer 19

^ is B

Answer 20

for B the year would be 2005, so x = ?

Answer 21

2002 is for A, which makes x = 2, what about B?

Answer 22

Yeah..I think I did something wrong with this equation

Answer 23

remember, x=0 mean 2000, that means x=1 is 2001, x=2 is 2002, x=3 is 2003 and so on

Answer 24

y = 1630(8) + 13190

Answer 25

thats for 1b, which means y = ?

Answer 26

y= 13040 + 13190
y = 26230

Answer 27

26230 = profit.

Answer 28

yep you got it :D

Answer 29

Although...?

Answer 30

$26230

Answer 31

Where did '5- 2" from the upper equation used to solve 1a come from?

Answer 32

that is from "X-x", where X = 5 for 2005, and x = 2 for 2002

Answer 33

Why did they need to be subtracted from each other?

Answer 34

Why did "5-2" have to happen? Why is that relevant?

Answer 35

What is B - A?

Answer 36

What..?

Answer 37

What is equation B minus equation A?

Answer 38

2005 - 2002? --> Used 5 from 2005, and "2" from 2002?

Answer 39

I don't know. That's why I'm asking you.

Answer 40

What is equation A and equation B? you should know this by now.

Answer 41

but, if you just want to understand the X-x part, then you have to understand what the slope m of an linear equation means

Answer 42

it means the rate of change of y with respect to x

Answer 43

Yes I know. But..

Answer 44

I'm very frustrated. I was just wondering if you could solve the equation, (and just the equation) and give me step-by-step explanations.

Answer 45

Your teaching methods..aren't helping me...that much. No offense.......

Answer 46

To solve for the slope m, just compute
m = (Y-y)/(X-x)
where Y and X are from one linear equation, while y and x are from the other.

then substitute m back into anyone of those two equations, to solve for b, and you get the equation that you want.