ElectricPavlov

c/t = 4/7   

gave away 1/5c    and 2/3 t

1/5 ( 4) / ((2/3)(7)

4/5  /  14/3

12 / 70   = 6:35      is  C:T       T:C = 35:6

Here ya go....I did the first line....see if you can follow the example to do the rest

y + 3/5 = - x     in point -slope form

Slope = ( -4-2)/(7- -1) = -6/8 = -3/4

Point slope form is then   (pick either point)

y-2 = -3/4(x +1)

cookie = m cents

cake = cookie + 70    =   m+70

a)

2 *cake + 4* cookie

= 2* (m+70)   + 4*m

= 6m+140

b)   m = 80     so  cookie = 80 cents     and cake = m+70 = 80 + 70 = 150 cents

    3 * cake   + 2*cookies

    3* 150     + 2 * 80 = 610 cents

       If Alison is 25 cents short   she has   610 - 25 =  585 cents

19  17

18  18

17  19

are the only rolls out of    20^2    that produce  36    

              3/400

We need point P that is 1 /(1+2) = 1/3 of the way from P to Q

  for x    from 4 to 10        1/3 of the way would be   6

  for y    from  5 to 14        1/3 of the way would be  8                    (6,8)

(sqrta x +3)^2 = ax^2 + 15x + 9     expand the binomial on the L side

 ax^2 + 6 sqrt a + 9 = ax^2 + 15x + 9

so    6sqrt a = 15

          sqrt a = 2.5

          a = 6.25

If you don't count Pluto ( or the three other dwarf planets)  as a planet (many do not)     8 * 8 = 64 planets 

This from WolframAlpha ....I do not know how to derive it ( except for the decimal approximatio listed):