Sarah is building a 10-foot-long pen for her pet rabbits. She wants to make gravel bases for two circular food containers to go inside the pen along its width, as shown in the diagram. Let y represent the width of the pen and x represent the radii of the gravel bases and food containers. She knows that the gravel bases need to fit entirely inside the pen, so the sum of the diameters of the gravel bases cannot exceed the width, y. Sarah has at most $150 to spend on materials. The cost will be $4.00 per linear foot of fencing and $2.00 per square foot of the gravel bases (the cost of the gravel at 1 inch of depth). Write the system of inequalities that can be used to determine the length and width of the pen and the radii of the gravel bases for the food containers. Use the diagram of the pen and containers above to help. Base your inequality statements on the given information.
