(proportions) the ratio of green marbles to pink marbles is 3: 7. determine the number of green marbles if there are 84 pink marbles.

So porportions are just fractions.
Green/Pink, which in this case equals 3/7. This means that for every 3 green marbles, there are 7 pink.

Now we plug in what we know. 84 pink. So this is: x/84, x because we don't know how many green there are.

Using 3/7 we can now solve this because: 3/7=x/84. That's how porportions work.

Now we cross multiply: 84•3=7x
252=7x or 7x=252.

We need to isolate x, so divide: x=252/7
x=36.

OR we can do it this way

3/7=x/84

How many times greater is 84 than 7?: 84/7=12. 12 times greater.

So if the bottom is 12 times the 7 than the top has to be 12 times 3. 3x12=36.

The first option is better for porportions, but the second option is goo for smaller numbers.

Either way we get that there are 36 green marbles.