Question

One summer you charge \(\$ 20\) to mow a lawn and \(\$ 10\) to trim bushes. You want to make \(\$ 300\) in one week. An algebraic model for your earnings is \(20 x+10 y=300,\) where \(x\) is the number of lawns you mow and \(y\) is the number of bushes you trim. Solve the equation for \(y\).

Short answer

The solution to the equation for \(y\) is \(y = 30 - 2x\).

Step-by-step solution

Write down the original equation

The original equation is \(20x + 10y = 300\). It represents the amount of money earned from mowing lawns and trimming bushes in a week.

Isolate y term

This can be achieved by subtracting the term 20x from both sides of the equation. This leaves \(10y = 300 - 20x.\)

Solve for y

The final step is to divide both sides of the equation by 10 to solve for y. This results in \(y = 30 - 2x\).