ElectricPavlov

Say there are 24 boards         1/4 = 6 red boards

     so 2/3 of the scooters are red  = 6 also            then total  scooters = 9      *** edited *** (for clarity-- answer does not change)

24 + 9 = 33 total items            12 of the total (6+6)  are red 

                                 33 f = 12      f = fracton of total        f = 12/33 = 4/11 of the total are red

r=1                  <<<<<<<<<

Say there are 24 boards      1/4 = 6 red boards

     so 2/3 of the scooters = 6 also           then red scooters = 9

24 + 9 = 33 total items            12 are red       33 f = 12      f = fracton of total        f = 12/33 = 4/11 of the total are red

Just pic the point exactly between:    x   2 to 6         4

                                                         y   3 to 8          5.5

Multiply R side by   -1/-1   then eliminate the denominator from both sides to get:

2 sqrt z - 3  +sqrtz -1   = 1-3 sqrt z

6 sqrt z = 5

sqrt z = 5/6

z = 25/36

The number of units sold is dependent on the price

   starts at 24     with price   8

       as price rises by 1      units goes down by 3

             units sold then becomes   (24 - 3(x-8) )     =  48 - 3x

                   PROFIT is  number of units sold * price   - units sold * cost

                                              (48-3x)             * x          -    (48-3x) *   4            <=====simplify this

                                                    -3x^2 + 48x            -192 + 12x

                                a)      PROFIT = -3x^2 + 60x - 192    

                                b)   Max occurs at - b/2a =  -60 / (-3*2)  = 10 dollars  price

                                c )  -3(10^2) + 60(10) - 192 = 108 dollars  profit                                              

Use the distance formula between two points to calculate the distance....this is ONE SIDE of the square.....Multiply this times 4 for the perimeter.

At LEAST 5    means  5  or 6  or 7   or 8  or   9  or 10  could have been Heads ....

10c5   + 10c6    + 10c7   + 10c8   + 10c9   + 10c10 = ______________

4/5 g   =   3/4 r       this is given.

re-arrange to   g = 15/16 r

then

(g - 105 )  / (r-102)  = 5/6 

g-105   =  5/6 (r-102)          sub in the red equation

15/16 r  - 105  = 5/6 r  - 85

r = 192     then using the red equation again  g = 180   for a total = 372 apples originally

     then he sold 105 + 102

         372 - ( 105+102) = 165 aplles left

I guess you do not know 'Chuckie' is a nickname for 'Charles'  as is 'Charlie'  and  "Chuck".....      get a life.....