A restaurant offers the possibility of 168 three-course dinners. Each dinner has an appetizer, an entrée, and a dessert. If the number of appetizers decreases from 7 to 5, how many fewer possible three-course dinners can the restaurant offers?

1 Answer
MathFact-orials.blogspot.com
Mar 23, 2017

120

Explanation:

Let's look at it this way:

Before the change is made, there are 168 three-course dinners possible. How can we achieve that number? We have Appetizers, Entrees, and Desserts. We can reach 168 by saying:

#AxxExxD=168#

We know there are 7 appetizers, so #A=7#, and so:

#7xxExxD=168#

#ExxD=24#

We can now multiply in the new number of appetizers, #A=5#:

#5xx24=120#

~~~~~~~~~~

Notice that we could have simply said:

#168/7xx5=120#

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