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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?

Verified Answer :

naǫ

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.

\(x+4x+0.5x=33 \\ 5.5x=33 \\ x=\frac{33}{5.5}=\frac{330}{55}=\frac{30 \times 11}{5 \times 11}=\frac{30}{5}=6 \\ \\ 0.5x=0.5 \times 6=3\)

There are 3 blue marbles.

apologiabiology

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

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