Question

emma is planning a surprise party. She is considering using one of two venues. The banquet of hall A will cost $862 fot a reservation, plus $76 per dinner. The banquet of hall B will cost $75 per dinner, in addition to $894 for the reservation. In order to make the best decision , Emma figures out-How many guests it will take to have the venues cost the same amount? What woyld the total cost be? How many guest would it be?

Answer 1

Ok for this problem, there are 2 equations representing hall A and hall B

hall A:  y=76x+862 where x=number of dinners and y=total cost

hall B:  y=75x+894 for the same variables

To find where the 2 meet, simply substitute one equation into the other, creating:  76x+862=75x+894

Solving this, we find that x=32, so at 32 guests, the cost would be the same

For part 2, put the answer for part 1 into either equation from the start, so y=76(32)+862, or y=3294

And we already found that x=32, which represents the # of guests