SOLUTION: 2 Using Desmos : Luke is starting a landscaping business and will cut lawns. His startup cost to purchase two lawn mowers is $450. He will use $1 in gas for each lawn and will ch

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Question 1208482: 2 Using Desmos :
Luke is starting a landscaping business and will cut lawns. His startup cost to purchase two lawn mowers is $450. He will use $1 in gas for each lawn and will charge $10 per lawn.
a) Write a linear system to represent this problem. Remember to define your variables
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Maybe you can use Desmos on your own, but description feels like you want an equation for finding
profit for a number of lawns served. The cost of the lawn mowers just happens once. The revenue
from the lawns would happen more than just once, so this formula may be incomplete:

x, number of lawns
y, the profit



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
2 Using Desmos : 
Luke is starting a landscaping business and will cut lawns. His startup cost to purchase two lawn mowers is $450. He will use $1 in gas for each lawn and will charge $10 per lawn.

a) Write a linear system to represent this problem. Remember to define your variables 

With number of lawns to be mowed being x, we get revenue EQUATION as: R(x) = 10x 
                                                    Cost EQUATION as: C(x) = x + 450
These are the required equations for your system.

As you may know, Profit = Revenue - Cost. So, in this case, Profit = R(x) - C(x)
                                                            Profit = 10x - (x + 450) = 10x - x - 450 = 9x - 450

And, BREAK-EVEN units occur when R(x) = C(x), or in this case, 10x = x + 450
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