Keith had 694 green, yellow and blue marbles altogether. he had 3 times as many blue marbles as yellow marbles. there were 90 fewer green than blue marbles. how many blue marbles did keith have?

Let  the number of green, the number of yellow and the number of blue marbles respectively.

We have

(we will call this equation 1)

Also, (yellow marbles are three times as many as blue marbles), so equation 1 becomes



But, (green marbles are as many as blue marbles - 90)
and because , we have that

So, equation 1 is now




We add 90 to both sides so



We divide each side by 7, so finally



and we have


and


To check if our results are correct, we can see that

,

so we are indeed correct.