CPhill

We are trying to maximize

P = 450x + 80y

Subject to these  constraint equations:

x ≥ 0,  y ≥ 0,  5x + 20y ≤ 400   and  10x + 15y ≤ 450 ..... where x is the number of chairs produced and y is the number of tables produced

Well...I'm not a "professional"....or even a "sub-professional".......more like a "recreational mathematician"......but.....I'll do my best.....!!!

I assume you want to find the number of each type of stamp.

Let x be the number of US stamps and y be the number of foreign stamps

So we have

x + y = 12

And the statement....The number of U.S stamps is 3 less than twice the number of foreign stamps.....can be written as

x + 3 = 2y

So using the first equation, we can let  y = 12 - x....so...in the second equation, we have

x + 3  = 2(12 -x)   simplify

x + 3 = 24 - 2x     add 2x to both sides and subtract 3 from both sides

3x = 21     divide by 3 on both sides

x = 7    which implies that y = 5

So, he has 7 US stamps and 5 foreign stamps....

(1 + 1)  is just 2 in any of these bases.....!!!!

I assume you want to start with .02, double every successive day, and calculate the sum at the end of the year.....(Warning..it's  huge  number..!!)

WolframAlpha gives the final sum as

To write it without scienific notation, just move the decimal point to the right 108 times....!!!!

This is an "alternating" series ... we have

4 = 7/ [1 - (- r)]  = 7/(1 + r)   and solving for r, we have

4 = 7 / (1 + r) → (1 + r) = 7/4 → r = 3/4

And the form of this series is ..  ∑ 7 *(-3/4)^(n-1)   from 1 to infinity

And the result of dividing the third term by the second term is just (-3/4)  .... as we would expect....!!!!

Nice one, saseflower...!!!

The age of a man 3 years ago was 11 times the age of his son. The ratio of their ages after 15 years will be 2:1

And I assume you want to find their current ages??

Let x and y be the son's and father's ages, now...so we have

11(x-3)  = y-3 →   11x - 33 = y - 3  →   11x - 30 = y    (1)

2(x + 15) = y + 15 →  2x + 30 = y + 15 →  2x + 15 = y

And setting the "y's" equal, we have

11x - 30 = 2x + 15  rearrange

9x = 45   solve for x

x = 5, and that's the son's age now

And using (1)

11(5) - 30 = y  = 25  and that's the father's age now

2 Many

Sasini meant to type "width" rather than "weight'.....