John wants to plan a big party for his parents' 25th anniversary. Jill's Catering charges $100 to rent their building and $30 per dinner. El Sombrero charges $150 to rent their facility and $25 per plate. For how many guests will the cost be in the same at the two caterers?

Question

anonymous · Answer

The sum is the same and is presented like this:
S = initialFee + guests * costPerGuest

S(Jill) = 100 + 30x
S(Sombrero) = 150 + 25x

100 + 30x = 150 + 25x
5x = 50
x = 10

Test drive:
10 guests at Jill's will cost 100 + 30 * 10 = 400
10 guests at the Sombrero will cost 150 + 25 * 10 = 400

anonymous · Answer

After that Sombrero is cheaper of course, 11 guests at Jill's for 430 vs Sombrero's 425.

anonymous · Answer

And for <=9 Jill's was cheaper.