Intermediate Algebra Tutorial 11


Intermediate Algebra
Answer/Discussion to Practice Problems  
Tutorial 11: Practice Test on Tutorials 7 - 10


WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 11: Practice Test on Tutorials 7 - 10


Problems 1a - 1c:  Solve for the variable.

 
1a. problem 1a

checkAnswer:

ad1a2
 
 

1b. problem 1b

checkAnswer:

ad1b
 
 

1c. problem 1c

checkAnswer:

ad1c
 

Be careful on this one.  Remember that you can divide into 0.  0 divided by anything is 0.  So the answer is a = 0, NOT no solution.  If you were trying to divide by 0, for example -17/0, then the answer would be no solution.
 
 

Problems 2a - 2c:  Solve the word problem.

 
2a.  The product of 5 and a number is 8 less than 7 times that number

checkAnswer:
 

Step 1: Understand

Make sure that you read the question carefully several times. 

Since we are looking for a number, we will let 

x = a number
 

Step 2: Devise a Plan (Translate)

ad2a1
 

Step 3: Carry out the plan (solve)

 
ad2a2

 
Step 4: Look back (check and interpret)

If you take 5 times 4, it is 8 less than 7 times 4.  So, this does check.
 

FINAL ANSWER:  The number is 4.
 
 
 

2b.  The sum of 3 consecutive integers is 234.  Find the integers.

checkAnswer:
 

Step 1: Understand

Make sure that you read the question carefully several times. 

We are looking for 3 consecutive integers, we will let

x = 1st consecutive integer

x + 1 = 2nd consecutive integer

x + 2  = 3rd  consecutive integer
 

Step 2: Devise a Plan (Translate)

ad2b1
 

Step 3: Carry out the plan (solve)

 
ad2b2

 

Step 4: Look back (check and interpret)

If you take the sum of 77, 78 and 79, you do get 234.
 

FINAL ANSWER:  The three consecutive integers are 77, 78 and 79.
 
 
 
 

2c.   You are wanting to buy a stereo system that costs $325 plus tax.  If you are going to be taxed 8.25%, how much will be the final cost of the stereo system? (round to the nearest cent)

checkAnswer:
 

Step 1: Understand

Make sure that you read the question carefully several times. 

Since we are looking for the final cost of the stereo system, let

x = the final cost
 

Step 2: Devise a Plan (Translate)

ad2c1
 

Step 3: Carry out the plan (solve)

 
ad2c2

 

Step 4: Look back (check and interpret)

If you add on 8.25% of 325 to 325 you do get 351.8125.
 

FINAL ANSWER:  The final cost is $351.81.
 
 
 
 

Problem 3a:  Solve the equation for the  specified variable.

 
3a. problem 3a  for y

checkAnswer:

ad3a
 
 

Problems 4a - 4b:  Solve the following word problems.

 
4a  You are traveling down I-40 at a constant speed of 70 mph.  How many hours will it take you to travel 385 miles?

checkAnswer:
 

Step 1: Understand

Make sure that you read the question carefully several times. 

Since we are looking for how long it would take you to travel, we can use the distance/rate formula:

d = rt

The variables in this formula represent the following:

d = distance
r = rate
t = time
 

Step 2: Devise a Plan (translate)

In this problem, 
d = 385
r = 70
t =  ? = this is the variable we are looking for

d = rt

Plugging the values into the formula we get:

385 = 70t
 

Step 3: Carry out the plan (solve)

 
ad4a

 

Step 4: Look back (check and interpret)

If you go a rate of 70 miles per hour for 5.5 hours, you would travel 385 miles.
 

FINAL ANSWER:  It would take 5.5 hours.
 
 
 

4b.  A farmer has three cylindrical shaped containers to hold feed in.  Each container has the same radius of 3 feet and height of 4 feet.  What is the total volume of the three containers?

Hint: the volume formula for a cylinder is cylinder

checkAnswer:
 

Step 1: Understand

Make sure that you read the question carefully, several times. 

Since we are needing to find the volume of a cylinder,  we can use this formula:

cylinder



The variables in this formula represent the following:

V = volume of a cylinder
r = radius
h = height
 

Step 2: Devise a Plan (translate)

In this problem, 
V = ? = this is the variable we are looking for
r =
h = 4

cylinder

Plugging the values into the formula we get:

ad4b1 
 

Step 3: Carry out the plan (solve)

First, find the volume of a cylinder
 

ad4b2

 
Each cylinder has a volume of 36example 2bcubic feet  or approximately 113.04 cubic feet.  If there are three of them, then we need to multiply this volume by 3.

 
ad4b3

 

Step 4: Look back (check and interpret)

If you take 4example 2b times 3 squared, you do get 36example 2b, so the volume checks out.  If you take 3 times 36example 2b, you do get 108example 2b, so the volume for three cylinders checks out.
 

FINAL ANSWER:  The total volume for three cylinders is 108example 2bcubic feet  or approximately 339.12 cubic feet.
 
 

Problems 5a - 5c :  Solve, write your answer in interval notation and graph the solution set.

 
5a. problem 5a

checkAnswer:

ad5a1
 

Interval notation:  (-inifinity, 10)

Graph:
ad5a2
 
 

5b. problem 5b

checkAnswer:

ad5b1

Interval notation: [2/5, inifinity)

Graph:
ad5b2
 
 
 

5c. problem 5c

checkAnswer:

ad5c1

Interval notation:  (12, inifinity)

Graph:
ad5c2
 

 

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WTAMU > Virtual Math Lab > Intermediate Algebra >Tutorial 11: Practice Test on Tutorials 7 - 10


Last revised on July 3, 2011 by Kim Seward.
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