Question 174·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis
A workbench stands on 4 identical feet. When the workbench is empty, it puts equal pressure on each foot, and the pressure on each foot is 8 pounds per square inch.
When a 60-pound box is placed on the workbench, the total weight is still distributed equally among the 4 feet, and the pressure on each foot becomes 9.5 pounds per square inch.
Which choice is the area, in square inches, of the bottom of each foot that is touching the floor?
When a rate (like pressure in pounds per square inch) changes after adding a known amount, write one equation for each situation using the same unknown area. Convert each pressure statement into a force-per-foot equation, then eliminate the unknown total weight by substitution or subtraction to solve quickly for the area.
Hints
Use the definition of pressure
Pressure is force divided by area. Here, the force on one foot is the total weight divided by 4.
Create two equations with the same area
Write one equation for the empty workbench and a second equation for the workbench with the 60-pound box.
Eliminate the workbench’s weight
After rewriting both equations, subtract or substitute so the unknown workbench weight cancels, leaving only the foot area.
Desmos Guide
Model each situation as a line
Let represent the foot area and let represent the workbench weight .
Enter the two equations:
Find the intersection
Tap the intersection point of the two lines. The -coordinate of the intersection is the value of (the area of one foot).
Step-by-step Explanation
Write pressure equations for each situation
Let be the area (in square inches) of the bottom of one foot, and let be the weight (in pounds) of the empty workbench.
Because the weight is shared equally, each foot supports pounds when empty and pounds with the box.
Pressure (force on one foot)(area), so:
Clear fractions and express weight in terms of area
Multiply each equation by :
Multiply each equation by 4:
Eliminate and solve for
Substitute into :
Subtract from both sides:
Divide by 6 to get . Therefore, the area of the bottom of each foot is 10 square inches.