SOLUTION: you are organizing a dance. Let a be the fixed cost (the cost before you include any people, for example the rental of a facility, decorations etc.) and b be the cost per person. (

Question 995387: you are organizing a dance. Let a be the fixed cost (the cost before you include any people, for example the rental of a facility, decorations etc.) and b be the cost per person. (a.k.a food, snacks etc.) Suppose you know it costs $1400 for 50 people and $2600 for 100 people.
set up a system of 2 equations in terms of a and b
Found 2 solutions by josgarithmetic, macston:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
y, the dance cost, depends on x number of students.

The variables are being used differently from what is typically used in discussing slope-intercept form. HERE, "b" is the slope, and "a" is the vertical axis intercept. Your points are still used in the regular form of (x,y).

Once that is well understood, then form these equations for a system:

Observe how this uses the points given, (50,1400) and (100,2600).

You can most comfortably use the Elimination Method if you want to solve for a and b.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
x=number of people; y=total cost
.
y=a+bx
.
$1400=a+50b
$1400-50b=a
b=(a-$1400)/(-50)
.
$2600=a+100b
$2600-100b=a
b=(a-$2600)/(-100)
.
$1400-50b=$2600-100b
50b=$1200
b=$24
.
(a-$1400)/(-50)=(a-$2600)/(-100)
-100a+$140000=-50a+$130000
$10000=50a
$200=a

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