# Bowling Alley Costs

### Linear Systems

## Made By: Amitoze Deol

## Situation

Lea is having a Christmas party. She wants to have her party in a bowling alley. Lucky Strike Lanes charges $125 for rental and decoration, with an additional cost of $8 per each person attending. On the other hand, Thunder Lanes chardes charges $250 for rental and decoration, with an additional cost of $3 per person attending.

## Equation

Let

*P*represent the number of people attending. Let*C*represent the cost.Lucky Strike Lanes:

*C= 125+8p*

Thunder Lanes:

*C= 250+3p*

## Table of Values

## Point of Intersection of Equations

Lucky Strike Lanes: C=125+8p

Thunder Lanes: C=250+3p

Point of Intersection:

125+8p=250+3p

8p-3p=250-125

5p=125

5p/5=125/5

p=25

We can substiture 25 as p and solve for C which is the cost, using the equation: 125+8p

y=mx+b

C= 125+8×25

C=125+200

C=325

Therefore the point of intersection is (25,325)

## Bowling Cost per Number of People

## Graph

Y Axis- Cost

X Axis- Number of People Attending

Blue Line- Thunder Lanes

Red Line- Lucky Strike Lanes

## Solution

Therefore, the cost in each bowling alley will be the same if there are 25 people attending. The cost of having her party with 25 people attending will be $325 for both Thunder Lanes and Lucky Strike Lanes. However, if Lea is inviting less than 25 people, it would cost her less to have her party at Lucky Strike Lanes. On the other hand, if she is inviting more than 25 people, if would cost her less to have her party at Thunder Lanes.