80 POINTS Gavin is moving into a new apartment that has a kitchen with an area of 50 square feet. If the area of the kitchen is 10 square feet more than the area of the bedroom, what is the area of the bedroom?

Complete the steps below to find the area of Gavin’s bedroom.

Part A
Let the variable b represent the area of the bedroom. Write an equation in terms of b to represent Gavin’s situation.

Part B
What is the first step in solving the equation you wrote in part A? Explain.

Part C
Rewrite the equation from part A to complete the first step.

Part D
What is the second step in solving the equation you wrote in part A? Explain.

Part E
Rewrite the equation from part C to complete the second step.

Part F
Recall the method that the video showed to solve Gavin’s word problem. The video showed how we can use numerical expressions (with the help of a diagram) to arrive at a solution.

Compare the expression method from the video with the equation method that uses the variable b. Do both methods use the same sequence of operations?

Part G
What does your answer to part F imply? Explain.