A town's total allowance for firefighter's wages and benefits in a new budget is $600,000. If wages are calculated at $40,000 per firefighter and benefits at $20,000 per firefighter, write an equation whose solution is the number of firefighters the town can employ if they spend their whole budget. Let x represent the number of fire fighters they higher.

Answer 1

To set up the equation for the budget spent on firefighters' wages and benefits, we can define the following:

• Let \( x \) be the number of firefighters.
• The total cost for wages per firefighter is $40,000.
• The total cost for benefits per firefighter is $20,000.

The total cost for one firefighter (wages + benefits) can be expressed as:

\[ \text{Total cost per firefighter} = \text{Wages} + \text{Benefits} = 40,000 + 20,000 = 60,000 \]

Now, the total cost for \( x \) firefighters can be expressed as:

\[ \text{Total cost for } x \text{ firefighters} = 60,000x \]

The town's total budget for firefighter wages and benefits is $600,000. Therefore, we can set up the equation:

\[ 60,000x = 600,000 \]

This equation represents the relationship between the number of firefighters \( x \) and the total budget of $600,000.

To find the number of firefighters the town can hire, you can solve this equation for \( x \):

\[ x = \frac{600,000}{60,000} = 10 \]

Thus, the town can employ 10 firefighters if they spend their whole budget.