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

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.

a: 1/6, j: 1/4

step-by-step explanation: you are welcome

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet