Question

The fee for a banquet hall is $525 for a group of 25 people and $1475 for a group of 75 people. Included in the fee is a standard set-up charge. What is the fee per person?

$16
$18
$19
$20

Answer 1

Okay, so I guess they also want to figure out the set up charge also- this is going to be a 2 variable equation.

X is the fee per person, and y is the set up charge.

25x+ y= 525

75x + y= 1475

So what you need to do is pick an equation, then isolate x:

25x + y= 525

25x= 525 -y

x= (525 - y)/25

Then, plug this in for x in the other equation:

75x + y= 1475 (original problem)

75((525 - y)/25) +y =1475 (subbed in x from other equation)

(75*525 -75y)/25 +y=1475 (distributed 75) (also could be multiplying fractions; 75/1)

(39375- 75y)/25 +y = 1475 (next I am simplifying the fraction)

1575 -3y +y = 1475 (Subtracting 1575; combining y's)

-2y = -100 (divide both sides by -2)

y=50

Okay, so now we know what the set up charge is- let's plug it into the unaltered first equation. (Note: At this point, you could really sub it into either equation and solve for x.)

25x+ y= 525

25x + 50 = 525

25x= 475

x= 19

Let's double check by subbing in y to the other equation as well:

75x + y= 1475

75x +50= 1475

75x= 1425

x= 19

Yay! It checks out in both problems!

Hope this helps, make sure to get a good night's sleep still.

Answer 2

The Answer is 20 I believe