This document contains solutions to 8 math problems. Problem 1 asks to find the length of a square given its area is 50 times its perimeter. The length is found to be 200 units. Problem 2 asks to find the length and width of a room given its area of 96 ft^2 and that the width is 4 ft less than the length. The length is 12 ft and width is 8 ft. The document provides the general 3 step process of choosing variables, writing equations, and solving for the unknowns.

2. Is it true that 1 = 2?

4. Problem 1: The area of a square is numerically
equal to fifty times its perimeter. Find the
length of a side of the square.
Solution:
Step 1: Choose a variable to represent
what is unknown.
Let 𝒔 be the length of the side of a
square

5. Step 2: Translate what you are seeing in words into
Mathematical expressions. Meaning, write the equation
based on the given information

6. Step 3: Simplify the expression and solve for the
unknown
Since the length of a square
could not be zero hence, the
length of the side of the
square is 200 units.

7. Problem 2: Jose purchased carpet to cover the
floor of a rectangular room that has an area of
96 ft2 . The width of the room he is carpeting is
4 feet less than the length. Find the length and
width of the room.
Solution:
Step 1: Choose a variable to represent
what is unknown.
Let x be the length Let x -4 be the width

8. Step 2: Translate what you are seeing in words into
Mathematical expressions. Meaning, write the equation
based on the given information
Problem 2: Jose purchased carpet to cover the floor
of a rectangular room that has an area of 96 ft2 . The
width of the room he is carpeting is 4 feet less than
the length. Find the length and width of the room.

9. Step 3: Simplify the expression and solve for the
unknown
Since a measurement cannot
be negative, the length is 12 ft.
To find the width, substitute 12
for x: x – 4 = 12 – 4 = 8 The
width is 8 ft.

10. Example 3: The length of a rectangle is three times the
width. If the area of the rectangle is 432 m2, find the length
and width.
Problem 4: The area of a square is 25𝑦2 − 100𝑦 +
100 square units. What is the length of the side?
Problem 5: The length of a rectangular table is 8 more
than the width. If the area is 180 𝑚2, find the length
and the width.

12. Problem 6: The product of two consecutive
integers is 110. Find the value of the
integers.
Solution:
Step 1: Choose a variable to represent
what is unknown.
Let x be the first integer
Let x + 1 be the second integer

13. Step 2: Translate what you are seeing in words into
Mathematical expressions. Meaning, write the equation
based on the given information
Problem 6: The product of two consecutive
integers is 110. Find the value of the
integers.

14. Step 3: Simplify the expression and solve for the
unknown

15. Problem 7: The product of two
consecutive integers is 210. Find all
such pairs of integers.
Problem 8: The product of two
consecutive even integers is 120. Find
all such pairs of integers.