Part to whole ratio word problem using tables

We're told that one month the ratio of indoor to outdoor play times for Yusuf's class was two to three. They had 30 total play times. How many of the play times were indoors? How many were outdoors?

Pause this video and see if you can figure that out.

All right, now let's work through this together, and I'm going to figure this out by setting up a little bit of a table. So we have our indoor play times. I'll write it out. Play times. We have our outdoor play times, outdoor play times. Then we have our total play times, total play times.

And then let me set up a table here, as promised. And then I'm going to set up two columns here. So the first column is going to concern itself with the ratios, so this is the original ratio. And here we're going to put the actual counts, actual counts.

So, what information do we know? We know that the ratio of indoor to outdoor is two to three. So the ratio of indoor to outdoor is two to three. And then we can also think about what would be the ratio of either of these to total play times.

Well, for every two indoor play times, there are three outdoor play times. That means for every two indoor play times, there are five total play times; or for every three outdoor play times, there are five total play times.

And now let's think about what we know about the actual counts. They tell us that there was a total of 30 actual play times. So this is the actual number: 30.

Now this is useful because now we can think about how do we go from the original ratios to the actual counts. If we take the total, we notice that we are multiplying by six. So to maintain the ratios, we would want to multiply everything by six.

So if you multiply this by 6, you're going to have 12 actual indoor play times. And if you multiply this by 6, you're going to have 18 actual outdoor play times.

And notice the ratio still holds up: 2 is to 3 as 12 is to 18; or 2 is to 5 as 12 is to 30.

And so there we have it. We know how many of the play times were indoors: 12, and how many were outdoors: 18.