Interpreting unequal ratios

We're told that Akeem's recipe for blackened catfish uses 19 grams of their favorite blend of ground pepper for every four catfish fillets. Tisha uses 25 grams of the same blend of ground pepper to cook six catfish fillets. Assuming the fillets are the same size, whose fillets have a stronger pepper taste?

So pause this video and see if you can work that on your own before we do this together.

All right, now let's do this together. So for Akeem, the ratio of the ground pepper to fillets is 19 grams for every four fillets. For Tisha, it is 25 grams for every six catfish. So what we want to do is say, all right, who has more grams maybe for a given amount of fillets?

So unfortunately, they don't give us the same amount of fillets. Here we have four fillets, and here we have six fillets. But what if we set up a table where we just try to make each of them make more and more fillets, and we just see how much of the ground pepper each of them will use?

If we get to a point where they're using the same amount of fillets, then if one of them is using more ground pepper, there’s going to be a stronger pepper taste. So let's say this is Akeem right over here, Akeem, and this is Tisha.

This is grams of pepper, so pepper in grams, and this is fillets. Then this is for Tisha, pepper in grams, and this is fillets.

So we already know that when Akeem were to make exactly four fillets, then they're going to use 19 grams. If let's keep going from there. If we double the amount of fillets, well, we're going to double the amount of grams; we're going to get to 38 grams if we were to add another four fillets to that.

So now we're at 12 fillets. Well, what's that going to be? To go from four to 12, you multiply by three. Well, that means you take that 19 and multiply by three.

Let's see, that would be 30 plus 27; that would be 57. Maybe this is enough. Let's see what we can do for Tisha right over here. So when Tisha makes six fillets, then she's going to use 25 grams.

What if we double it to 12 fillets? This is interesting because we have 12 fillets here. Well, then we would double the pepper to 50 grams. So we have set up actually a really nice comparison.

If Akeem makes 12 fillets, they're going to use 57 grams of pepper, while if Tisha makes the exact same number of fillets, they're going to use only 50 grams of pepper. So for 12 fillets, Akeem would clearly use more pepper and therefore would have a stronger pepper taste.

So Akeem's fillets have the stronger pepper taste.