SOLUTION: You can have the party at a pizza place for $8 per person plus $30 for favors and a small cake or at a taco place for $12 per person plus $14 for a large cake. How many childre

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: You can have the party at a pizza place for $8 per person plus $30 for favors and a small cake or at a taco place for $12 per person plus $14 for a large cake. How many childre      Log On


   



Question 879835: You can have the party at a pizza place for $8 per person plus $30 for favors and a small cake or at a taco place for $12 per person plus $14 for a large cake.
How many children would you have to invite to the party for the cost to be less at the pizza place?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of children at party
Let +C+ = total cost of party
At pizza place:
+C+=+8n+%2B+30+
At taco place:
+C+=+12n+%2B+14+
-----------------
Find +n+ that will make the cost, C+
of the 2 places equal
+8n+%2B+30+=+12n+%2B+14+
+4n+=+16+
+n+=+4+
---------------
If 1 more child is invited, the +n+=+5+
At pizza place:
+C+=+8n+%2B+30+
+C+=+8%2A5+%2B+30+
+C+=+70+
At taco place:
+C+=+12n+%2B+14+
+C+=+12%2A5+%2B+14+
+C+=+74+
-------------
When 5 children are invited, the cost becomes less
at the pizza place
Here are plots of the 2 equations:
+graph%28+400%2C+400%2C+-1%2C+7%2C+-10%2C+100%2C+8x+%2B+30%2C+12x+%2B+14+%29+