The ratio of green marbles to Yellow marbles in Toby's bag is equal to 2/3 what percent of the marbles in the bag are green marbles

Answer 1

We are given that

# of green marbles / # of yellow marbles = 2/3

It is therefore also true that

% of marbles that are green / % of marbles that are yellow = 2/3

Let's use variables instead of re-typing those phrases. Define

% of marbles that are green = x

% of marbles that are yellow = y

Now we can rewrite the previous equation as:

x / y = 2/3

I have 2 unknowns and 1 equation, so i need another equation. Since x and y are percentages (and i can assume there aren't any other colored marbles in the bag), it is also true that

x + y = 100

Solve one of the equations for x, then plug into the other, or do the same thing for y. In any case, the equations yield

x=40

y=60

So 40% is the answer.