Question

3.) A caterer charges $120 to cater a party for 15 people and $200 for 25 people. A.) Write an equation using x and y to find the cost of having a party catered depending on the number of people attending. B.) Describe what the x and y variables represent in your equation. C.) Use your equation to predict how much it will cost to have a party of 40 people catered. Show your work.

Answer 1

Answer: A) The equation can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope represents the cost per person and the y-intercept represents the fixed cost. Using the two given points, we can find the slope and y-intercept:

(15, 120) and (25, 200)

m = (200 - 120) / (25 - 15) = 80 / 10 = 8

b = 120 - 8 * 15 = 120 - 120 = 0

So the equation is y = 8x.

B) In the equation y = 8x, x represents the number of people attending the party and y represents the cost of having the party catered.

C) To predict the cost of having a party of 40 people catered, we plug in x = 40 into the equation:

y = 8x

y = 8 * 40

y = 320

So it will cost $320 to have a party of 40 people catered.

Explanation: