A catering fi rm charges a fi xed cost for overheads and a price per person. It is known
that a party for 20 people costs $557, whereas a party for 35 people costs $909.50.
What is the fixed cost and the cost per person charged by the company?
To find the fixed cost and the cost per person charged by the catering firm, we can set up a system of equations based on the given information.
Let X represent the fixed cost and Y represent the cost per person.
From the first piece of information, we know that a party for 20 people costs $557. This can be expressed as an equation:
20Y + X = 557
From the second piece of information, we know that a party for 35 people costs $909.50. This can also be expressed as an equation:
35Y + X = 909.50
Now we have a system of two equations:
20Y + X = 557
35Y + X = 909.50
To solve this system of equations for X and Y, we can use the method of substitution or elimination. Let's use the method of elimination.
Subtracting the first equation from the second equation, we eliminate X:
(35Y + X) - (20Y + X) = 909.50 - 557
Simplifying the equation:
15Y = 352.50
Dividing both sides by 15:
Y = 23.50
Now that we have found the cost per person (Y), we can substitute this value back into one of the original equations to solve for X.
Let's substitute Y = 23.50 into the first equation:
20(23.50) + X = 557
Simplifying the equation:
470 + X = 557
Subtracting 470 from both sides:
X = 557 - 470
X = 87
Therefore, the fixed cost charged by the company is $87, and the cost per person is $23.50.
pretend you are given two points (20,557) and (35,909.5)
and your equation is
y = mx + b, where y is the cost , m is the price per person, and b is the fixed overhead.
sub in the two points and you have two equations in two unknowns.
Carry on from there.