Question

What is the cost of a party for 100 people at the vine house hotel

Answer 1

Answer:

1) The first 100 people @ $1750 ... $1750  

2) 30 more people @ $20 ea ..... $600  

------------ ----------------- ---------------------  

60 people ....... ...... ....... ..... ......$1350  

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  

For 100 people  

1) First 30 people @ $750 ........ $  750  

2) 70 more people @ $20 ea .... $1400  

-------- ------------ ------------- ----- -------------  

100 people ....... .......... ....... ..... $2150  

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  

This situation can be modeled by  

y = mx + b  

"b" in this case is the starting cost of $750 for up to 30 people.  

This means that there is one flat rate for any number of people up to 30.  

For any number of people up to 30 people, the fixed flat rate is $750.  

Examples:  

 1 person ... $750  

10 people ... $750  

25 people ... $750  

30 people ... $750  

------------  

Then there is a charge of $20 each for every person above that first 30.  

So the equation is  

y = mx + b <-- b is the fixed start cost of $750  

y = mx + 750  

Then there is a charge of $20 for each extra person, so that is  

$20 × "x" ( <-- the number of extra people)  

So the equation is  

y = total cost  

m = $20 for each extra person  

x = the number (whatever it may be) of extra people (a variable number of people)  

b = the starting fixed cost of $750  

y = mx + b  

y = 20x + 750  

This equation says:  

y (the total cost)  

= (equals)  

20 ($20 per each)  

x (each extra person)  

+ (in addition to)  

750 (the fixed starting cost of $750)  

----------------  

You can test this equation for 100 people to see if you get the same answer as before ($2150)  

y = mx + b  

y = 20x + 750  

y = 20 × 70 + 750  

y = 1400 + 750  

y = 2150 <-- same answer  

-----------  

The value of using the equation is that it is good for any number of people:  

For 121 people, the equation is  

y = 20x + 750 where x = 91 extra people  

For 28 people, the equation is  

y = 0x + 750 (no extra people, just the flat fixed start fee)  

-------------------------------  

Using C and P for y and x:  

C (total cost)  

=  

20P ($20 ea for each extra person over 30)  

+  

750 (the cost of the first 1-30 people)  

Hey hope this helped! :)

Answer:  

C = 20P + 750