Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 11: Practice Test on Tutorials 7  10
Problems 1a  1c: Solve for the variable. 
1c.
Answer:
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 Answer: 
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)

Step 3: Carry out the plan (solve) 
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. Answer: 
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)

Step 3: Carry out the plan (solve) 
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) Answer: 
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)

Step 3: Carry out the plan (solve) 
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. 
Problems 4a  4b: Solve the following word problems. 
4a You are traveling down I40 at a constant speed of 70 mph.
How many hours will it take you to travel 385 miles? Answer: 
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) 
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
Answer: 
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:
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 = 3
h = 4
Plugging the values into the formula we get:

Step 3: Carry out the plan (solve)
First, find the volume of a cylinder 
Each cylinder has a volume of 36 cubic
feet or approximately 113.04 cubic feet. If there are three
of them, then we need to multiply this volume by 3. 
Problems 5a  5c : Solve, write your answer in interval notation
and graph the solution set. 
5a.
Answer:
Interval notation: (,
10)
Graph:

5b.
Answer:
Interval notation: [2/5, )
Graph:

5c.
Answer:
Interval notation: (12, )
Graph:

Last revised on July 3, 2011 by Kim Seward.
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