CPhill

See my answer here : https://web2.0calc.com/questions/pat-has-two-sheets-of-large-square-stamps_1

Area of rectangle  =   product of the dimensions

(x - 2) (2x + 5)   =  8x  - 6      simplify

2x^2  - 4x + 5x   -10   = 8x   -  6        rearrange as

2x^2 + x -10  = 8x -  6

2x^2 - 7x - 4   =  0           factor  as

(2x + 1)  ( x - 4)   =   0

We need a positive value for x   .....the second factor  set to  0   will give us that

x  - 4 =   0

x =  4

See the proceedure here :   https://web2.0calc.com/questions/pls-help-again#r2

The tosses are independent events.....on  each toss he has a probability  of 1/2 of getting either color

So

P(blue) * P(blue)  =   (1/2) * ( 1/2)   =     1/4

Let E be what he earns per month

So

E - 120   - 95  =

E - 215            is what he has left after   the food and  transport

And then he spends  (2/5) of what's left

(2/5)(E -215)

So

(E  -215) - (2/5) (E - 215)  = 780

(3/5)  (E -215)  = 780

E  -  215  =  780 (5/3)

E  - 215  =  1300

E =  1300 + 215  =   $1515

S +  M  =  59  (1)

M + I    =   52 (2)

S + I   =   41   (3)

Subtract  (3)  from (1)

M - I    =   18     (4)      and

M + I  =    52     (2)

Add (4) and (2)

2M =  70

M  = 35

S + M = 59

S + 35 = 59

S = 59 - 35  =  24

M + I   = 52

35 + I  = 52

I  = 52  - 35   =   17

a + b  =   24   ⇒    b = 24  - a

So

2ab + 10a  = 3b + 257

2a (24 -a) + 10a  = 3(24 -a) + 257

48a  -2a^2 + 10a  = 72 - 3a + 257        rearrange as

2a^2 - 61a +  329    = 0         factors as

(2a  - 47) ( a - 7)    = 0         

The second factor set  = 0   gives an  integer for "a"

a - 7  =  0 

a =7

b = 24  - 7  =17

ab  =  (7)(17)   =   119 

P (4 green peppers)  =   C(5,4) * C (10,2)  / C(15 ,6)    = 45  /1001

P(5 green pepers)   = C(5,5) * C(10,1)  /C(15,6)    =  2 /1001

Total probability   =  [45 + 2]  /1001  =   47 /1001

Let  x  be the number of $12 increases

R =  Tickets sold *  Cost per ticket

R =  ( 40000 - 500x) ( 200 + 12x)

R =  8000000 - 100000x + 480000x - 6000x^2

R  =   -600x^2 + 380000x + 8000000

The  number of  $12 increases  (which is an integer ) that max the revenue =   [  -380000 / [ 2(-6000)] ] = 31 + 2/3    ≈  32

The cost per ticket that maxes the revenue ≈   (200 + 12 *32)  ≈ $584

We can choose  any 4 of the 9   people to be on  1 of the 3 teams

And then we can choose any 4 of the 5 remaining people to be on 1 of the remaining 2 teams

The last person is on the last team by default

So

C ( 9,4)  * C ( 3,1) * C(5,4) * C (2,1)  =   3780  ways

Not totally confident about this, but BuiderBoy  will  probably have the correct answer  !!!!  (LOL !!! )