Question

Tamera wanted to have a pizza/arcade birthday party. At Chuckecheese, it cost $50 to rent the birthday room plus $4 for each guest. At Pizza Zone, it cost $80 to rent the birthday room but only $2 for each guest. How many guests does Tamera have to have to justify going to Pizza Zone?

Answer 1

Chuckycheese :
50 to rent + 4 for each guest (g) ...... 50 + 4g

Pizza Zone :
80 to rent + 2 or each guest.....80 + 2g

In order for Pizza Zone to be a better deal, it has to be less then Chuckcheese
50 + 4g > 80 + 2g -- subtract 2g from both sides
50 + 4g - 2g > 80 -- subtract 50 from both sides
4g - 2g > 80 - 50 -- combine like terms
2g > 30 -- divide both sides by 2
g > 15

So this is saying that there has to be more then 15 guests for Pizza Zone to be less the Chuckycheese.
Lets check that...
50 + 4g > 80 + 2g......sub in 16 for g
50 + 4(16) > 80 + 2(16)
50 + 64 > 80 + 32
114 > 112 (correct)

so basically, Tamera can justify going to Pizza Zone if she brings along more then 15 guests....so she can bring 16 or more guests.