Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 8: 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
Find 72% of 35. 
Make sure that you read the question carefully several times.
Since we are looking for a number, we will let
x = the number

Answer/Discussion
to 1c
A local furniture store is having a terrific sale. They are marking
down every price 45%. If the couch you have our eye on is $440 after
the markdown, what was the original price? How much would you
save if you bought it at this sale? 
Make sure that you read the question carefully several times.
Since we are looking for the price of the couch before the markdown,
we will let
x = the price of the couch


*Combine like terms (1  .45 = .55)
*Inv. of mult. by .55 is div. by .55

If you subtract the 45% markdown form 800 you do get 440.
FINAL ANSWER:
The original price is $800.
You save 800  440 = $360.
(return to
problem 1c) 
Answer/Discussion
to 1d
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 1d) 
Answer/Discussion
to 1e
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 = one 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 1e) 
Answer/Discussion
to 1f
The sum of 3 consecutive odd integers is 57. Find the integers. 
Make sure that you read the question carefully several times.
We are looking for 3 ODD consecutive integers, we will let
x = 1st consecutive odd integer
x + 2 = 2nd consecutive odd integer
x + 4 = 3rd consecutive odd
integer


*Combine like terms
*Inv. of add 6 is sub. 6
*Inv. of mult. by 3 is div. by 3

If you take the sum of 17, 19 and 21 you do get
FINAL ANSWER: The three consecutive odd integers are 17, 19 and 21.
(return to
problem 1f) 
Answer/Discussion
to 1g
The cost C to produce x numbers of VCR's is C = 1000 + 100x.
The VCR's are sold wholesale for $150 each, so the revenue is given by R = 150x. 
Make sure that you read the question carefully several times.
We are looking for the number of VCR's needed to be sold to break even,
we will let
x = the number of VCR's 

*Get all the x terms on one side
*Inv. of mult. by 50 is div. by 50

Last revised on July 1, 2011 by Kim Seward.
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