CPhill

We can use a proportion to solve this

2 / 25   =    x / 60      cross-multiply

120 = 25x      divide by 25 on both sides

120/25 =  x  =  24/5    =     4.8 inches

a^2 = 74.1     take the square root of both sides

a   = √74.1   ≈ 8.61 rounded to two decimal places  {to be fair, "a" could have also been the negative of this, as well..} 

5/6+1/4 =     getting a common denominator, we have

20/24 +  6/24   =  26/24   =   13/12

This is a broad topic that obviously can't be covered in a concise answer.  This may get you started:

No, Alan...I worked it out, too....there's no "whole" number answer possible based on the available info........

Let x =  initial number red      ....the (3/2)x = initial number blue  ....  y=  initial  number green 

Before the sale, we have:

x + (3/2)x   + y = 1686         →              (5/2)x + y = 1686     (1)

After the sale, we have:

(1/2)x + (1/4)(3/2)x + y = 922       →     (7/8)x + y =    922      (2)

Subtract (2) from (1)

(13/8)x = 764       x =  about 470   initial red

(3/2)x =  about 705  initial blue

Rats!!!.....heureka beat me to it  !!!!!

Let's take it step-by-step......

[3y - 5] / 6 = [2y - 1]/ 3 + 2       multiply through by the common denominator of 6.....so we have

3y - 5   = 2[2y - 1]  + 12   simplify

3y - 5  =  4y - 2 + 12

3y - 5   = 4y  + 10         subtract 3y, 10 from both sides

-15 = y

[2x] / [ x + 3]  = 7     multiply both sides by x + 3

2x =  7 [x + 3]     simplify

2x = 7x + 21        subtract 7x from both sides

-5x  = 21       divide both sides by  -5

x = -21/5

Let x be the amount James had this morning

Then his sister had 2x  and his brother had x + 27

After his sister pays James and his brother 12 dollars each, she has 2x - 24 dollars and his brother has x + 27 + 12   dollars......and his brother has twice as much as his sister....so we have.....

2(2x - 24)  =  x + 27 + 12   simplify

4x - 48 =   x + 39    simplify

3x  = 87       divide both sides by 3

x = 29     this is what James had before his sister pays him $12.....so he has             $[29 + 12]  = $41, now

Check :

James' sister starts with $2(29) =  $58 

And his brother starts with $[ 29 + 27 ]=  $56

After the sister pays both brothers $12......

She has  $[58 - 24 ]  = $ 34   and James's brother has  $[56 + 12 ] =  $68  ......  and his brother has twice as much as his sister......!!!

[ 3x + 12 ] /  [ x + 4 ] =  [4x^2 + 8x + 8x^2] / [ 2x]     simplify and combine terms

3[ x + 4] / [ x + 4 ]  =  [ 12x^2 + 8x] . [2x] 

3   =  4x [ 3x + 2 ] ] [2x]

3  = 2[3x + 2 ]

3  = 6x + 4      subtract 4 from both sides

-1   = 6x        divide by 6 on both sides

-1/6 =  x