Unit Three: Problem Solving Task
Home Improvement Project
You are going to help finish the basement in your house. You will build three separate rooms: a family
room, a home office, and a laundry room. First you must develop a plan for the project. You don’t
have to worry about windows and doors now – just divide the space into the three rooms. You know
the following:
 The area of the basement is 1,680 square feet
 The width of the basement is 28 feet
 You mom wants the laundry room to be square
 The other two rooms will have equal lengths
Use expressions and equations to help plan the new spaces.
1. Write an algebraic expression to represent the length of the basement in terms of the lengths of
each of the rooms.
2. Using the area of the basement, write an equation that could be used to solve for the equal lengths
of the family room and the home office.
3. Use this equation to determine the lengths of the family room and the home office. Show all of
your steps. With the lengths, sketch a drawing of the plan for the basement. Be sure to label the
rooms and their lengths and widths.
4. There are two ways to write the equation – one way uses the distributive property and the other
does not. Look at you own equation. If you used the distributive property, write an equivalent
equation that does not use the distributive property. If you did not use the distributive property,
write an equivalent equation that uses it.
5. Use your revised equation to determine the lengths of the family room and the home office. Show
all your steps. How does this answer compare to your answer in problem 3?
Unit Three: Problem Solving Task
Home Improvement Project
You are going to help finish the basement in your house. You will build three separate rooms: a family
room, a home office, and a laundry room. First you must develop a plan for the project. You don’t
have to worry about windows and doors now – just divide the space into the three rooms. You know
the following:
 The area of the basement is 1,680 square feet
 The width of the basement is 28 feet
 You mom wants the laundry room to be square
 The other two rooms will have equal lengths
Use expressions and equations to help plan the new spaces.
1. Write an algebraic expression to represent the length of the basement in terms of the lengths of
each of the rooms.
2. Using the area of the basement, write an equation that could be used to solve for the equal lengths
of the family room and the home office.
3. Use this equation to determine the lengths of the family room and the home office. Show all of
your steps. With the lengths, sketch a drawing of the plan for the basement. Be sure to label the
rooms and their lengths and widths.
4. There are two ways to write the equation – one way uses the distributive property and the other
does not. Look at you own equation. If you used the distributive property, write an equivalent
equation that does not use the distributive property. If you did not use the distributive property,
write an equivalent equation that uses it.
5. Use your revised equation to determine the lengths of the family room and the home office. Show
all your steps. How does this answer compare to your answer in problem 3?