Question

Medals

Tabitha is renting a ballroom for an upcoming dinner reception. The rental fee for the ballroom includes a base price plus the cost of dinner per person. The table below shows the cost of the ballroom rental in relation to the number of people attending the dinner reception.


No. of Attendees 25 50 75
Total Rental Cost $500 $725 $950

What is the base price for the ballroom rental?


A. $275


B. $55


C. $9


D. $225

Answer 1

In this problem trial and error can work since it has so few variables.. it gives you the total cost and the number of people attending..so the answer choices represent the base rental. So take each of the answers and subtract it from the base cost. Then divided that into the number of people left.
For example

take 225 away from 950 and you are left with 725 and divide that by 75 . You get 9.6667 . If you take it from each of the others you find out that the answer is different each time. That makes the answer incorrect. Now you use the other 3 answers and do the same thing. The one that is correct will give the same answer each time.

Answer 2

Use two of the 3 given pieces of information to find a linear equation.
In other words, what is the equation of the line that contains
points (25, 500) and (75, 950) in slope-intercept form?
The intercept is the fixed fee, and the slope is the per-person cost.

Answer 3

what do they mean by base number?

Answer 4

I don't know, thats way I put it up here

Answer 5

do what spectrum did...sounds right.

Answer 6

@thomaster @Compassionate @Preetha @nincompoop

Answer 7

hey need help

Answer 8

Yes please

Answer 9

ok i say its b but i could be wrong

Answer 10

Do you know how to find the equation of a line given two points?
That's what you need to do here.

Answer 11

To get the answer to this you need to subtract each answer choice from the given price then divided each by the number of people. The correct answer will give you the same answer for all 3 sets. We can start with a larger number.

D. 950- 225 / 75 = 9.6667
725- 225 / 50 = 10
500-225 / 25 = 11

D is not the same answer all the way through ...so its incorrect.

B. 950-55 /75 = 11.933
725-55/50 = 13.4

You can see the next answer isn't correct here soyou can scrap B as well.

C. 9 dollars doesn't really make sense as a ballroom rental so you can pretty much safely assume it is out, but if you don't care for deduction you would find out it is incorrect as well. leaving A. 275

Just to Check it

A. 950-275/ 75 = 9
725-275/ 50 = 9
500-275/ 25 = 9

Answer 12

Meaning ...9 dollars per person. with a base rental of 275 dollars. Hope this helps

Answer 13

the base price is the starting price per person
but this type of pricing usually leads to discounted or custom pricing
let us say the base price per person is 10 bucks up to 50 people
so that would be 10 x 50 = 500
then additional people or person would be at a lower (discounted) price
this is kind of pricing usually ensures profit while at the same time competitive with pricing

Answer 14

the answer is A

Answer 15

950 - 725 = 225
225 for 25 people would mean 9 bucks a person
9*75 = 675
then
950 - 675 = 275 as your base price

Answer 16

check:
9*50 = costx + baseprice = 725

Answer 17

@Spectrum 's answer is correct, but his method works because this is a multiple choice question. If you were not given choices, this is how you'd solve it.

The data you are given fall in a straight line. Use two given points to find the equation of the line.

Let's use (25, 500) and (75, 950).

\( y = mx + b\)

\(m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{950 - 500}{75 - 25} = \dfrac{450}{50} = 9 \)

The slope, m, is 9.

Now we use the slope and one point and the slope-intercept form of the equation of a line to find the equation of the line. Let's use (25, 500).

\(y = mx + b\)

\(500 = 9(25) + b\)

\(500 = 225 + b\)

\(b = 275\)

\(y = 9x + 275\)

As I mentioned above, the slope is the cost per person, and the y-intercept is the fixed fee.

The answer is $275. Choice A.

Answer 18

Thank you for all the help every one it was helpful