Ratio word problem examples

What we're going to do in this video is tackle some word problems involving ratios.

So here we're told that Yoda Soda is the intergalactic party drink that will have all of your friends saying, "Um, good this is." You are throwing a party and you need five liters of Yoda Soda for every 12 guests. If you have 36 guests, how many liters of Yoda Soda do you need?

So pause this video and try to figure it out on your own.

Well, they tell us the ratio of liters of soda to the number of guests. So you need five liters for every 12 guests; that is the ratio. But we want to have 36 guests. So if the ratio is 5 liters of soda for every 12 guests, but we're in a situation where we have 36 guests, this is three times as many guests. We're gonna need three times as many liters of soda.

So three times five is fifteen. Five to twelve; five liters for twelve guests, or four; five liters for every 12 guests is the same thing as 15 liters for every 36 guests.

So to answer that question, how many liters do you need? You need 15 liters.

Let's do another one of these. Here we just have a picture of a bunch of fish in a tank, and it says there are eight big fish for every blank small fish. Then it says there are four big fish for every blank small fish. So pause this video again and see if you can work through this.

All right, so let's just count the big fish first. So there's one, two, three. Let me see, count this way: one, two, three, four, five, six, seven, eight. So in this tank, there actually are eight big fish.

Now, let's see how many small fish there are. There's one, two, three, four, five, six, seven, eight, nine, ten small fish. So in the tank, for every eight big fish, which you see in red, there are ten small fish. But here it says there are four big fish for every blank small fish, so what would that be?

Well, one way to think about it is we have half as many fish; we have half as many big fish. So we divided by two. We're going to have half as many small fish. So we’re gonna divide by two. So for every four big fish, there are five small fish.

One way to think about it: you could divide the fish evenly into two groups right over here. So let's see if we can capture that. If you could have this: if I divide it like that, here I have one, two, three, four big fish and one, two, three, four, five small fish.

Then in this group, I have one, two, three, four big fish and one, two, three, four, five small fish. So every four big fish there are five small fish. These are equivalent ratios.

Let's keep going. So here we're told an ice cream shop uses the following ingredients to make one sundae. They use two scoops of ice cream, four spoonfuls of sprinkles, and two tablespoons of whipped cream. How many sundaes did the shop make if they used 32 spoonfuls of sprinkles?

So pause the video and try to think about it. So there are a couple of ways to think about it here. It says, let's see, we're talking about sprinkles, so that's what's relevant here: four spoonfuls for every one sundae.

So we could say that the ratio of spoonfuls to sundaes is four to one. Four spoonfuls of sprinkles... let me write this way, let me write sprinkles. How many spoonfuls per one sundae? But here we're talking about using 32 spoonfuls of sprinkles, so that is eight times as many.

So you're going to be able to create eight times as many sundaes. So you're going to have 32 spoonfuls of sprinkles for every eight sundaes.

So how many sundaes did the shop make? Well, they made eight.

Let's do one last example. At a dog park, there are 10 black dogs, 5 brown dogs, 2 white dogs, and 12 multi-colored dogs. For every one brown dog, there are two blank dogs. Pause the video and figure out what goes in this blank.

All right, so let's see. There's five brown dogs for every ten black dogs, five brown dogs for every two white dogs, and five brown dogs for every 12 multi-colored dogs. But here you're saying for every one brown dog, there are two blank dogs.

So what type of dog is their ratio? For every brown dog, there's twice as many of that type of dog. Well, here we see for every five brown dogs, there are 10 black dogs. So one way to think about it, the number of black dogs is always going to be twice the number of brown dogs.

So for every one brown dog, there would be two black dogs. One way to think about it: the ratio between brown dogs and black dogs, and it's kind of counterintuitive. I used the wrong colors here; I should use brown and black, so let me do that.

So the ratio of brown to black is five brown dogs for every ten black dogs. Or if you divide both of these numbers by five, you would get one brown dog for every two black dogs. And that's exactly what this statement is saying.