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Equivalent Ratios and Proportions a la Shmoop

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Well Bobo is having two of his chimp friends over

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for a nice casual banana dinner.

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He's already set the table and place a gourmet meal of

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five bananas per chimp on each plate.

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Ya know, bananas have a peel hehe

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Suddenly the door opens and twenty-two chips come flooding in.

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Bobo's buddy Bam-Bam says

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Hey, sorry. Brought a few guys from the office, hope you don't mind.

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Ok so now Bobo has to serve bananas to all these other chimps.

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Hopefully there are enough in his pantry.

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Using the same ration of banana to chimp that Bobo was using initially, how many bananas will he need now?

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Well this is a perfect example of equivalent ratios.

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We know exactly how many bananas will feed three chimps

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now we just need to figure out how many

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are needed to feed twenty three.

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And don't forget Bobo! These hungry hungry monkeys right?

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Ok so chimps aren't monkeys, you got us.

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Hope you're proud of yourself.

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All right, well the ration of bananas to chimps is fifteen to three.

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Since Bobo put out fifteen bananas to feed three chimps, got it?

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It simplifies to five to one, meaning one chimp eats five bananas.

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Now that there are twenty three chimps we can show the equivalent ration like this:

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where b is the number of bananas needed to feed everyone.

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Now we simply multiply on both sides of our equation

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to clear out the denominator.

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Well 23 x 5 = 115 and boom we've got our answer

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We could have done the same thing if we'd left our fraction unsimplified.

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In that case we would have had 15/3 and b/23

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multiplying both denominators away we get 3b = 345

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then divide both sizes by three and we get

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b = yep, still 115

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Well as it turns out, Bobo has 110 bananas in his pantry.

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He feeds everyone except Bam-Bam.

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Yeah, those two aren't speaking at the moment.

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Things are a little tense...

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