CPhill

Thanks to you too, heureka........that's two methods that I have to learn from......!!!!!

Thanks , again.....I haven't seen this before and the "fixed point" concept is a new one on me......your explanation was excellent....!!!!!

[BTW......I think Melody mentioned to me that the "new and improved" forum will not let you edit LaTex......!!!!........bummer....!!!! ]

OK,  Brodudedoodebrodude............got it!!!!........Thanks!!!!

[Shouldn't the " + "  sign in Step 2 of your original answer be a " -"   instead??? ]

Very impressive,  Brodudedoodebrodude......!!!!!!

I understand most of it, but I'm still unclear as to how you arrived at the " fixed point"  value of "30" in Step 2......could you elaborate on that????

4x+5(x-7)    distribute the 5 across the terms in the parentheses

4x + 5x - 35      combine like terms

9x - 35

There are 24 total animals and 4  are goats....so....

4 / 24 =  1 / 6

This means that out of every six animals, one is a goat.

6x-5>12x+1        add 5 to both sides, subtract 12x from both sides

-6x > 6               divide both sides by -6 and reverse the inequality sign

x < -1

The unit rate is the cost per gallon......it is given by :

Total cost / Total quantity = $6.50 / 3.50  = about $1.86 per gallon  [ rounded]

We have :

2 + .70x = ..75(x + 2)     whhere x is the number of pounds of the 70% mix

Simplify

2 + .70x = .75x + 1.5     subtract 1.5, .70x from both sides

.5 = .05x       divide both sides by .05

.5 / .05  =  x =  10 lbs of the 70% mix

And (x + 2)   = (10 + 2)  = 12 lbs. total

f(1) = 20

f(n)=3*f(n-1)-60

Using WolframAlpha, the generalized  "formula" for the "nth" term is :

f(n)  = (-10/3) (3ⁿ - 9)

So

f(10)  = (-10/3) (3¹⁰  - 9)  =  - 196,800