Answer to Question #238590 in Calculus for steve

Question

Venue A charges $5,000 to rent their banquet hall for a wedding plus an additional fee of $

69 per guest. Venue B has no hall rental fee but charges $139 per guest for a wedding. Let

g represent the total number of guests for a wedding. Set up and solve an inequality to determine the number of guests you would need to have in order for Venue B to be cheaper than Venue A. Be sure to include a concluding statement in the context of the problem.

Answer 1

cost function for venue A

$C.P_A= \$ [5000+69g]$

cost function for venue B

$C.P_B = \$139g$

for $C.P_B< C.P_A$

$\$139g<\$[5000+69g]\\ 139g< 5000 +60g\\ 139g-69g< 5000\\ 70g<5000\\ g< 500/7\\ g<71.4$

Since g must be an integer

$g≤71$

$\therefore$ The number of guests needed in order for Venue B to be cheaper than Venue A is 71 people or less.