Math Riddle??

Question

10 points to the person who explains it AND has the correct answer. Good luck :)

A box of 102 red, black, and blue beads has twice as many red beads as black, and six more blue than black. How many beads are black?

Answer 1

Where x represents black beads:

x + 2x + (6 + x) = 102
3x + 6 + x = 102
4x +6 = 102
4x = 96
x = 24

There are 24 black bead, 48 red bead and 30 blue beads.

Answer 2

choose one variable say x and use that for the # of black beads
it is best to set the variable as the thing you want to find out
# of black beads = x
the number of red beads is twice as many as black so
# of red beads = 2x
there are 6 more blue beads than there are black beads so
# of blue beads = x+6
the total number of beads is 102 so
x + 2x + x + 6 = 102
then you solve
4x + 6 = 102
4x = 96
x = 24
so there are 24 black beads

Answer 3

I used the equation red + black + blue = 102. Substituting all in terms of black, i got (2black) + (black) + (black + 6) = 102 to represent red,black, and blue respectively. Solving for black, the equation simplifies to 4blacks + 6=102. The answer is 24 black beads.

Answer 4

R=red, B=black, U=blue

R+U+B=102
R=2B
U=B+6

So,
2B+B+6+B=102
4B+6=102
4B=96
B=24

So,
U=30
R=48

Answer 5

Black = x
Red = 2x
Blue = x+6

x+2x+(x+6)=102
x+2x+x+6=102
4x+6=102
4x=96
x=24

24 black
48 red
30 blue