Algebra 1
Name: ________________________ Date:_________________2011
3.6 Equations and Problem Solving
A
To define one variable in terms of another.
I. PERIMETER. Draw a diagram to help you understand the problem.
a) The length of a rectangle is 6 inches more than its width. The perimeter of the rectangle is 24 inches.
What is the length of the rectangle?
b) The width of a rectangle is 3 inches less than its length. The perimeter of the rectangle is 26 inches. What
is the width of the rectangle?
c) The width of a rectangle is 2 cm less than its length. The perimeter of the rectangle is 16 cm. What are
the dimensions of the rectangle?
d) The width of a rectangle is one half its length. The perimeter of the rectangle is 66 m. What are the width
and length of the rectangle?
e) The length of a rectangular garden is 4yd more than twice its width. The perimeter of the garden is 68 yd.
What are the width and length of the garden?
II. CONSECUTIVE INTEGERS differ by _______.
Example:_______________________________
For consecutive integer problems, you must define a variable for the first integer and then define the other
unknown integers in terms of the first one.
Let:
𝑛
first integer
𝑛+1
second integer
𝑛+2
third integer
fourth integer
a) The sum of three consecutive integers is 147. Find the integers.
b) The sum of three consecutive integers is 72. Find the integers.
c)
The sum of two consecutive integers is −11. Find the integers.
d) The sum of three consecutive integers is −102. Find the integers.
e) The sum of three consecutive integers is 582. What are the integers?
III. CONSECUTIVE EVEN or ODD INTEGERS differ by _______.
𝑛
Example:___________________________
The first even or odd integer.
𝑛+2
The second even or odd integer.
𝑛+4
The third even or odd integer.
a) The sum of two consecutive even integers is 98. What are the integers?
b) The sum of two consecutive even integers is −150. Find the integers.
c)
The sum of two consecutive even integers is 242. Find the integers.
d) The sum of two consecutive odd integers is 68. Find the integers.
e) The sum of three consecutive odd integers is 75. Find the integers.
f)
The sum of two consecutive odd integers is −8. What are the integers?