Question

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?

Answer 1

so number of red is represented by r
number of green is represented by g
number of blue is represented by b

so r+g+b=33

there are 4 times as many red as green or
r=4g
there are half as many blue as green
1/2g=b or g=2b

so r+g+b=33
we can subsitute 1/2g=b for b
r+g+1/2g=33
subsitute r=4g for r in the equation
4g+g+1/2g=33
add like terms
5 1/2g=33
multiply both sides by 2
11g=66
divide both sides by 11
g=6

there are 6 green marbles

subsitute g=6 into r=4g and g=2b

r=4(6)
r=24
there are 24 red marbles

g=2b
6=2b
divide both sides by 2
3=b
threre are 3 blue marbles



there are 24 red marbles, 6 green marbles, and 3 blue marbles and 24+6+3=33
r=24
g=6
b=3

Answer 2

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 = 0.5x
There are 33 marbles in total, so x+4x+0.5x=33.


`x+4x+0.5x=33 \\ 5.5x=33 \\ x=(33)/(5.5)=(330)/(55)=(30 * 11)/(5 * 11)=(30)/(5)=6 \\ \\ 0.5x=0.5 * 6=3`

There are 3 blue marbles.