A bag of marbles has twice as many blue marbles as green marbles, and the bag has at least 54 marbles in it. At least how many green marbles does it have?
If we have twice as many blue marbles as green, we have 3 parts; 2 parts blue and 1 part greens. Therefore, 1/3 of the marbles are green
At least 18 of the marbles are green
[latex]b\ \ \ \rightarrow\ \ \ the\ number\ of\ blue\ marbles\\g\ \ \ \rightarrow\ \ \ the\ number\ of\ green\ marbles\\\\b+g \geq 54\ \ \ and\ \ \ b=2g\\\\2g+g \geq 54\ \ \ \Leftrightarrow\ \ \ 3g \geq 54\ \ \ \Leftrightarrow\ \ \ g \geq 18\\\\Ans.\ At\ least\ 18\ green\ marbles.[/latex]