Question

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

Answer 1

The original number of combinations is found from
7 * Ne * Nd = 168 ..............(1)
Where 7 is the number of choices of appetizer, Ne is the number of choices of entree and Nd is the number of choices of dessert.
The new number of combinations, x, is found from
5 * Ne * Nd = x .................(2)
Taking the ratio of (1) and (2)
\[\frac{7\times N _{e}\times N _{d}}{5\times N _{e}\times N _{d}}=\frac{168}{x}\]
which simplifies to
\[\frac{7}{5}=\frac{168}{x}\]
therefore the new number of combinations is\[x=\frac{168\times 5}{7}\]

Answer 2

THANKS!!!!!!!!!!!

Answer 3

You're welcome :)