SOLUTION: A caterer charges a fixed cost for preparing dinner plus a cost for each person served. You know that the cost for 100 people will be $750 and the cost for 150 people will be $1050

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A caterer charges a fixed cost for preparing dinner plus a cost for each person served. You know that the cost for 100 people will be $750 and the cost for 150 people will be $1050      Log On


   

Question 66766: A caterer charges a fixed cost for preparing dinner plus a cost for each person served. You know that the cost for 100 people will be $750 and the cost for 150 people will be $1050. Find the caterer's fixed cost and cost per person served.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let x=fixed cost for preparing dinner
And y=cost for each person served
Now we are told that the fixed cost (x) plus the total cost per person served (100y)equals $750. So our first equation is:
(1) x+100y=750
We are also told that the fixed cost (x) plus the total cost per person (150y) equals $1050. So we have our 2nd equation:
(2)x+150y=$1050
Subtract (1) from (2)
50y=300
y=$6 -----------Cost for each person served
Substitute y=$6 in (1)
x+100($6)=$750
x+$600=$750 subtract $600 from both sides
x=$750-$600=$150 Fixed cost of preparing dinner
CK
fixed cost($150) plus cost per person ($6)(100)=$750
$150+$600=$750
$750=$750


Also fixed cost ($150) plus cost per rerson (150)($6)=$1050
$150+$900=$1050
$1050=$1050

Hope this helps----ptaylor