Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 15: Introduction to Problem Solving
Answer/Discussion
to 1a
The sum of a number and 2 is 6 less than twice that number. 
Make sure that you read the question carefully several times.
Since we are looking for a number, we will let
x = a number


*Get all the x terms on one side
*Inv. of add 2 is sub. 2
*Inv. of mult. by 1 is div. by 1

If you take the sum of 8 and 2 it is 6 less than twice 8, so this does
check.
FINAL ANSWER:
The number is 8.
(return to problem
1a) 
Answer/Discussion
to 1b
A rectangular garden has a width that is 8 feet less than twice the
length. Find the dimensions if the perimeter is 20 feet. 
Make sure that you read the question carefully several times.
We are looking for the length and width of the rectangle. Since
width can be written in terms of length, we will let
L = length
Width is 8 feet less than twice the length:
2L  8 = width


*Mult. ( ) by 2
*Combine like terms
*Inv. of sub. 16 is add 16
*Inv. of mult. by 6 is div. by 6

If length is 6, then width, which is 8 feet less than twice the length,
would have to be 4. The perimeter of a rectangle with width of 4
feet and length of 6 feet is 20 feet.
FINAL ANSWER:
Width is 4 feet.
Length is 6 feet.
(return to problem
1b) 
Answer/Discussion
to 1c
Complimentary angles, sum up to be 90 degrees. Find the measure
of each angle in the figure below. Note that since the angles make
up a right angle, they are complementary to each other.

Make sure that you read the question carefully several times.
We are already given in the figure that
x = 1 angle
x + 30 = other angle


*Combine like terms
*Inv. of add 30 is sub. 30
*Inv. of mult. by 2 is div. by 2

If x is 30, then x + 30 = 60. 60 and 30 do add up to be 90, so they are complementary
angles.
FINAL ANSWER:
The two angles are 30 degrees and 60 degrees.
(return to problem
1c) 
Last revised on July 26, 2011 by Kim Seward.
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