Question

1. jack is going to buy a snowblower to start earning money in the winter. the function ( f(x)=25x - 300 ) represents the amount of money he will profit by snowblowing ( x )-driveways.

a. find ( p(20) ). ( p(20)=)
this means

b. solve for ( x ) if ( p(x)=500 ). ( x=)
this means

Explanation:

Step1: Calculate \(P(20)\)

Substitute \(x = 20\) into the function \(P(x)=25x - 300\).

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This means that when Jack snow - blows 20 driveways, his profit is $200.

Step2: Solve for \(x\) when \(P(x) = 500\)

Set up the equation \(25x-300 = 500\).
Add 300 to both sides of the equation: \(25x=500 + 300\), so \(25x=800\).
Divide both sides by 25: \(x=\frac{800}{25}=32\).
This means that Jack needs to snow - blow 32 driveways to make a profit of $500.

Answer:

a. \(P(20)=200\). This means that when Jack snow - blows 20 driveways, his profit is $200.
b. \(x = 32\). This means that Jack needs to snow - blow 32 driveways to make a profit of $500.