ElectricPavlov

Both stations have rising prices, but B is rising more slowly and is now  likely less than A ....so go to B .

FALSE     perpindicular lines cross at 90 degree angles

Day 1-4    go to station A        Day 5-7 go to station B        Day 8 could be anything, but I would likely go to B

(x - 1)^2 = -4 + 4x.          expand L side

x^2 -2x +1 = -4 + 4x        simplify

x^2 -6x +5 = 0                factor

(x-1)(x-5) = 0

x = 1 and 5

**** edit *****     corrected !

36 possible rolls

 1   x

 4   x

  x  1

 x   4         where x = 1-6      less  the  1-1  4-4 counted twice     AND the  1-4   4-1   counted twice   =    20 rolls out of 36         (Thanx, Alan !)

Yep, I believe you are correct..... there is a problem with the Q   AND my solution had a math error !   D'Oh !        ~ EP

Let's use the correct numbers (thanx , Guest !)

a = arthur now

(a-4) = 11 (j-4)      and     (a+4) = 4 (j+ 4) 

a = 11j -40                         11j-40 + 4 = 4j+ 16        shows j = 52/7      then a = 292/7 

                                                           check:    4 years ago   j = 24/7      a = 264/7         CHECK !

                                                           check     4 years from now   j = 80/7      a = 320/70     CHECK !

Now find when a is twice as old

11j-40 + x    =   2 ( j+x)

11(52/7) - 40   + x   = 104/7 + 2x

188/7 = x                  188/7 years from now   a   will be twice as old as   j        CHECK !

a = arthur now

(a-4) = 11 (j-4)      and     (a+4) = 4 (j+ 4) 

a = 11j -40                         11j-40 + 4 = 4j+ 16        shows j = 8          then a = 48

now find when he is twice as old as j

a + x   = 2 ( j+x)

48 + x = 2(8) + 2x

32 = x                                     32 years from now    arthur = 80   j = 40 y/o

I think you have to have even numbered exponents of all of the prime factors to get a perfect square....

   so you would need to multiply by   3 *5 * 7             ( the 9^9  = 3^18 )

Originally

r / y = 3/7      or    r = 3/7 y       and    y+r = 4          

                                                          y + 3/7 y = 4      shows   y = 4 * 7/10 = 2.8 gal      and red = 1.2 gal    

now add yellow to get  2/15

r / ( y+x)  = 2 /15  

1.2 / (2.8+ x )  = 2/15

1.2 (15/2) = 2.8 + x                    x =    6.2   gal of yellow to add