Red Rose Banquet vs. Elite Banquet

Time to Party!!

A family has decided to celebrate their daughter's sweet 16 at a banquet hall. They are debating over which banquet hall to book the occasion at, and they have narrowed down to "Red Rose Convention Center" and "Elite Banquet Hall." They want to celebrate their daughter's birthday in a colossal celebration, however, they must keep the costs of both banquets in mind. Both banquets charge a flat rate, plus an extra fee per plate. Red Rose Convention Center charges a flat fee of \$625, (includes decorations, service, props, etc.) plus \$35 per plate/person. Elite Banquet Hall charges a flat fee of \$550, (includes decorations, service, props, etc.) plus \$50 per plate/person. If the family is inviting 50 people, which banquet hall should they choose?

Equations in y = mx+b form

Let "p" represent the number of people.

Let "C" represent the total cost.

Red Rose Convention Center:

C = 35p + 625

Elite Banquet Hall:

C = 50p + 550

Graphic Solution:

Red point = Elite Banquet Hall

Blue point = Red Rose Convention Center

Solving the linear system

First, we start by placing an equal sign between the two equations, and solve for x.

35x + 625 = 50x +550

Next, bring the variables on one side and numbers on the other.

35x - 50x = 550 - 625

Solve for both sides.

-15x = -75

Divide both sides by -15, to find x.

-15x / -15 = -75 / -15

x = 5

To find y, substitute x as five for one of the equations.

y = 50 (5) + 550

y = 250 + 550

y = 800

Therefor, the point of intersection for the two lines is (5,800).

So, which Banquet Hall is Better?

The point of intersection for this linear system is (5,800). This means that the cost for five people at both banquet halls will be \$800. If you are inviting less than five people at your occasion, Elite banquet hall would be cheaper.This is not very reasonable, however, as banquet halls have a minimum requirement of 20 people. Since the family is inviting 50 people for their daughter's sweet 16, Red Rose banquet hall will be the cheaper option. For 50 people, Red Rose Banquet Hall charges \$2375 which includes the initial charge of \$625, and \$35 per plate. Contemplating with Elite banquet hall, for 50 people the total cost will be \$3050 (includes initial charge of \$550 and \$50 per plate). Red Rose Banquet hall is \$675 cheaper than Elite Banquet hall, and offers the same service, decorations, and props as well. Therefor, Red Rose Banquet Hall is the better option!!

What is the purpose of a Linear System?

A linear system serves as numerous purposes. It can be used to predict data, or merely infer information from the graph. It helps us track the rate at which the data increases or decreases. According to this situation, the linear system can help the family decide which banquet hall will help them save the most money.