## anonymous551 2 years ago I honestly don't understand how to solve linear word problems... Can someone help me solve one?

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1. anonymous551

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.)

2. findme

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?

3. findme

if you need farther help, ask :D

4. anonymous551

Um..I don't know..

5. anonymous551

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

6. findme

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?

7. anonymous551

Equation "B" as in finding the slope?

8. findme

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

9. anonymous551

Okay. I need clarification. My Algebra teacher solved this problem like this: |dw:1354175590461:dw|

10. anonymous551

Can you explain what she (teacher) did there?

11. findme

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)

12. findme

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

13. anonymous551

What is equation "A" & "B"?

14. findme

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

15. findme

"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?"

16. anonymous551

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

17. findme

18. anonymous551

Okay. y = 1630(2002) +13190

19. anonymous551

^ is B

20. findme

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

21. findme

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

22. anonymous551

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

23. findme

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

24. anonymous551

y = 1630(8) + 13190

25. findme

thats for 1b, which means y = ?

26. anonymous551

y= 13040 + 13190 y = 26230

27. anonymous551

26230 = profit.

28. findme

yep you got it :D

29. anonymous551

Although...?

30. findme

\$26230

31. anonymous551

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

32. findme

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

33. anonymous551

Why did they need to be subtracted from each other?

34. anonymous551

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

35. findme

What is B - A?

36. anonymous551

What..?

37. findme

What is equation B minus equation A?

38. anonymous551

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

39. anonymous551

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

40. findme

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

41. findme

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

42. findme

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

43. anonymous551

Yes I know. But..

44. anonymous551

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.

45. anonymous551

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

46. findme

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.

47. findme

which is y = mx + b, where m and b are the value found using the above method.