A drawer has some red, green, and blue marbles. There are 33 marbles.
There are 4 times as many red marbles as green marbles. There are half
as many blue marbles as green marbles. How many blue marbles are in
the drawer?

Green marbles = x.There are 4 times as many red marbles as green marbles, so red marbles = 4x.There are half as many blue marbles as green marbles, so blue marbles = 0.5xThere are 33 marbles in total, so x+4x+0.5x=33.[tex]x+4x+0.5x=33 \\ 5.5x=33 \\ x=\frac{33}{5.5}=\frac{330}{55}=\frac{30 \times 11}{5 \times 11}=\frac{30}{5}=6 \\ \\
0.5x=0.5 \times 6=3[/tex]There are 3 blue marbles.

so number of red is represented by rnumber of green is represented by gnumber of blue is represented by bso r+g+b=33there are 4 times as many red as green orr=4gthere are half as many blue as green1/2g=b or g=2bso r+g+b=33we can subsitute 1/2g=b for br+g+1/2g=33subsitute r=4g for r in the equation4g+g+1/2g=33add like terms5 1/2g=33multiply both sides by 211g=66divide both sides by 11g=6there are 6 green marblessubsitute g=6 into r=4g and g=2br=4(6)r=24there are 24 red marblesg=2b6=2bdivide both sides by 23=bthrere are 3 blue marblesthere are 24 red marbles, 6 green marbles, and 3 blue marbles and 24+6+3=33r=24g=6b=3