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?

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

Hello!

the answer is:

the correct option:

b.

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!