every marble in a jar has either a dot, a stripe, or both. the ratio of striped marbles to non striped marbles is 3:1, and the ratio of dotted marbles to non dotted marbles is 2:3. if six marbles have both a dot and a stripe, how many marbles are there all together?

Question

mathmate · Answer

Let 
s=number of striped marbles (includes both striped and dotted)
d=number of dotted marbles (includes both striped and dotted)
6=number of both
then 
d-6=number of non-striped marbles
s-6=number of non-dotted marbles
We have 
s/(d-6)=3/1  =>  s=3(d-6) ...(1)
d/(s-6)=2/3  =>  3d=2(s-6)  ...(2)
solve for s and d

To check your answer, number of striped is slightly less than twice the dotted ones, or put back you solutions into (1) and (2) and see if the equations hold.

anonymous · Answer

Let the number of marbles with a dot be $x$ and the number of marbles with a stripe be $y$. Then the number of non-dotted marbles is y+6 and the number of non-striped marbles is x+6. Employing the given ratios we have$$3(y+6)=x$$$$2(x+6)=3y$$Solve this system for $x$ and $y$, and add 6 to the total.

anonymous · Answer

Messed my system of equations up

anonymous · Answer

$$y+6=3x$$$$3(x+6)=2y$$That's better