I am planning to buy 10 solar panels to install on my roof. The installation cost is $150, and I want to ensure that the total cost, including the panels and installation, does not exceed $1000.

If the cost of a solar panel is $x, write an inequality in terms of $x$ that I could solve to find the maximum price I can afford for a solar panel while staying within my budget. Additionally, determine the maximum allowable cost per solar panel to meet my budgetary constraints.

The inequality that represents the situation is 10x + 150 ≤ 1000. Solving for x gives a maximum cost of $85 per solar panel to stay within the $1000 total budget.

Explanation:

The student is asking how to write an inequality to determine the maximum price they can pay per solar panel while staying within a total budget of $1000. The cost of installation is $150, and the student intends to purchase 10 solar panels.

To create the inequality, let's assign x to be the cost of one solar panel. The combined cost of the panels and the installation fee should be less than or equal to $1000. We express this as the inequality 10x + 150 ≤ 1000.

To find the maximum cost per panel, subtract the installation fee from the total budget, and then divide the result by the number of panels: (1000 - 150) ÷ 10 = 85. Therefore, the maximum cost per panel that the student can afford is $85.