Numbers - Elementary Math

John’s dad was walking in the car rental lot to pick up their rental car. He passed several spots on the left. They were numbered as follows:

201 203 205 207

Which number would he most likely see on the next parking lot on the left?

a. 200
b. 206
c. 209
d. 212

Answer : c

Why:
The student should notice the following:
a. The parking lot numbers are all odd numbers so the next number coming should be an
odd number.
and
b. Each parking lot number is increased by 2 from the previous number.

Therefore if we add 2 to the last number which is 207 we should get 209 as follows:
207 + 2 = 209

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Word Problem - College Level

Nancy can clean her room in 2 hours. It takes her brother Sam 3 hours to complete the same task. How long will it take them if they worked together to get the room cleaned?

Answer: 6/5 hours

Steps to solve the problem:

This problem can be solved when we assume that both Nancy and Sam are working at a constant rate which means that each of them does the same amount of work in the first hour as they do in the last hour.

To try and find the total hours it takes both of them, we must find how much work can each one of them do in 1 hour. Therefore if Nancy completes the cleaning job in 2 hours therefore in 1 hour she completes 1/2 of the work. Also, if Sam completes the job in 3 hours, then in 1 hour he completes 1/3 of the work.

If we let x = the total number of hours it takes for both of them working together, then in 1 hour, they must do 1/x of the time.

Lets put everything together as follows:

Amount of work done by Nancy = 1/2
Amount of work done by Sam = 1/3
Total amount of work = 1/x

Lets add the hours to get the total as follows:

1/2+1/3 = 1/x

The lowest common denominator is 6x. Therefore, both sides of the equation are multiplied by 6x as follows:

6x (1/2) + 6x (1/3) = 6x (1/x)
3x + 2x = 6
5x = 6
x = 6/5 = 1.2 hours

It will take them 6/5 or 1.2 hours to get the room cleaned together.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Square Roots - High School

Which of the following is equivalent to:

a. 36

b.

c.

d. 28

Answer: b

Why:

© Copyright 2007.Najwa S. Hirn. All rights reserved

Rectangles - 7th. Grade Math

The length of a rectangle is 3 times the width. The perimeter of the rectangle is 48 feet. What are the measurements for the length and width?

Answer:
Width = 6 ft.
Length = 18 ft.

Steps:
If the width of the rectangle = x
Then the length will be 3x
The formula for the perimeter of a rectangle = 2length + 2 width
Substituting the numbers we get:
48 = 2(3x) + 2x
48 = 6x + 2x
48 = 8x
x = 48/8 = 6
Therefore the width = 6 feet
The length = 3 (6 ft) = 18 feet

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Multiplication - Elementary Math

While visiting a chocolate factory, John was told that the factory produces 250 chocolate pieces per second. Based on this information, John’s teacher asked him to find out how many pieces of chocolate the factory can produce per minute.
Note: 1 minute = 60 seconds

a. 12,000
b. 15,000
c. 18,000
d. 21,000

Answer: b

Why:
This is a multiplication problem. If one minute = 60 seconds and we know that 250 chocolate pieces are produced per one minute then we must multiply that number by how many seconds are in one minute to get our answer as follows:

(60 seconds / 1 minute) x (250 pieces / 1 second) = 15,000 pieces / 1 minute

Don’t forget to cancel the units for seconds. At that point you are left with the number of chocolate pieces produced per one minute.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Word Problem - College Level

Linda is 4 years older than Allyson. Two years ago Linda’s age was three times Allyson’s age. Find the age of each girl now.

Solution: Allyson is 4 years old and Linda is 8 years old

steps:
Allysons age now = x
Linda’s age now = x + 4

Allyson’s age two years ago = x – 2
Linda’s age two years ago = x + 4 – 2 = x + 2

Also, two years ago Linda’s age was three times Allyson’s age = 3 (x-2)

In order to set up the equation, we equate the girl’s ages from two years ago and solve for x as follows:

x + 2 = 3 ( x – 2)
x + 2 = 3x – 6
Isolate the variable:
x – 3x = - 6 – 2
-2x = -8
x = -8/-2 = 4

Now we know that Allyson’s age now = 4 years old. We substitute for x to find Linda’s age:
Linda’s age = 4 + 4 = 8 yearls old.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Variables in an Equation - High School Math

When Sandra ordered candy for her store, she received three types of boxes containing the chocolate bars. The boxes are labeled x , y and z. If box x contains 10 bars, and box y contains 20 bars and box z contains 15 bars then the total number of bars is represented in the following equation:

T = 10x + 20y + 15z

If Sandra received 70 type x boxes, 30 type y boxes and 20 type z boxes, find the total number of bars she received?

Answer: 1600

Steps:
We must find out the total number of bars received in each box type as follows:
box x = 10 (70) = 700
Box y = 20 (30) = 600
box z = 15 (20) = 300

The total number of bars received will be the addition of all the above as follows:

T = 700 + 600 + 300 = 1600 chocolate bars.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Algebraic Thinking - Middle grades

JoAnn was hired as a book sales rep. Her hourly wage is $8.50 per hour. In addition, she is paid $3.50 bonus for each sale she makes. Which of the following expression represents how much she makes per week if she made 5 sales and worked n number of hours per week.

a. 5n(8.50 + 3.50)
b. 5(8.50n + 3.50)
c. 8.50n + (3.50 x 5)
d. (8.50 + 3.50) x (5 + n)

Solution: c

Why:
In order to solve this problem we must follow the steps below:
1) The amount that she earned from her job per week = 8.50 x n = 8.50n
2) The amount she earned per week by making 5 sales = 3.50 x 5
3) The total amount she would earn = The total of both of the above which will be:
8.50n + (3.50 x 5). Therefore this will be the correct expression.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Finding the Mean - Elementary Math

The numbers below show the grade each student received on the math exam:

Sam received 38
Adam received 40
John received 43
Katie received 45
Joy received 49

What was the mean number of grades the students received?

a. 35
b. 43
c. 48
d. 50

Solution: b

The Steps:
The mean value of any set of numbers indicates the average of those numbers. The average of the numbers is calculated by adding all the numbers and dividing them by how many times they occurred. For this example it will be as follows:
38 + 40 + 43 + 45 + 49 = 215
215 / 5 = 43
(see post 08-31 and 10-04)

For additional information on this subject go to : How to Find the Mean

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Polynomials - College Algebra

Expand the following Binomial:

The Solution:

The Steps:

The rule for taking the square of a binomial states that:
The square of a binomial is the sum of the square of the first term, twice the product of the two terms, and the square of the last term.
By using this rule, we can expand the above binomial as follows:

For additional information and examples, go to: Square Trinomials



© Copyright 2007.Najwa S. Hirn. All rights reserved.

Pythagorean Theorem - High School Math

In the following right angle triangle, side b = 13.5 and side c = 15.5 Calculate side a



http://www.flourmilling.net/maths.html

Answer: 7.6

Explanation:
To solve this problem we must use the Pythagorean theorem, which states:

Substituting the values for c and b in the above equation results in:

© Copyright 2007.Najwa S. Hirn. All rights reserved.

Angles - Grade 8

Joe’s new swimming pool is in the shape of a Pentagon such as the shape on the left. What is the value of each interior angle in this shape?
a. 108
b. 128
c. 148
d. 168

Answer: a

Explanation:
A Pentagon is a Polygon with five sides. This also means that it has five equal angles.
The formula used to find the sum of all the interior angles in any Polygon is as follows:
180 ( n-2) where n represents the number of angles in the polygon.
In this problem n will equal 5. Lets apply the formula to find the sum of all the interior angles:
180 (5-2) = 540
Since we have 5 angles, we can find the value of each angle by dividing as follows:
540 / 5 = 108 degrees is each interior angle in a Pentagon.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Weights and Measures - Elementary Math

Rachel weighed herself on the scale. Which one of the following measurements best describes her weight?

a. 80 inches
b. 80 pounds
c. 80 ounces
d. 80 tons

Answer: b

Explanation:
A person's weight is usually measured in pounds, so when Rachel weighed herself the scale showed her weights in pounds. Therefore, the correct answer will be 80 pounds.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Variations - College Level

If y, x and z are variables and K is a non-zero constant, write the algebraic equation that represent each of the following:

a. y varies directly with x
b. y varies inversely to x
c. y varies jointly with x and z

Answer:
a. y = Kx
b. y = K / x
c. y = Kxz

Explanation:
Variation problems usually appear in sciences such as physics and chemistry.
There are two types of variations: direct and inverse. A combination of those relationships creates other variations such as joint.
In a direct variation, when one variable such as (x) increases, that causes the other variable (y) to increase also. The same happens when one decreases thus causing the other one to decrease.
Therefore, in a direct variation, a change in one variable results in the same change in the other variable.
In an inverse proportion, an increase in one variable will result in a decrease in the other and thus the name inverse.
Therefore in an inverse proportion a change in one variable causes the opposite to happen to the other.
A combination of variations occurs also. When one variable varies directly with two variables, we say that it varies jointly.

©Copyright 2007.Najwa S. Hirn. All rights reserved.

Related Measures - High School Math

Janet burns 15 calories per minute on the treadmill. How many calories does Janet burn per one-hour?

a. 300 calories / hour
b. 800 calories / hour
c. 900 calories / hour
d. 1100 calories / hour

Answer: c

Explanation:
The answer is 900 calories / hour
One hour = 60 minutes.
Therefore, in order to find out how many calories Janet burns in one hour, we multiply the amount of calories she burns per minute (in this case 15) by the total minutes per hour, which are 60 as follows:

(15 calories / 1 minute) x (60 minutes / 1 hour) = 900 calories / 1 hour
Note that the units for minutes disappear and we are left with calories per hour.

©Copyright 2007.Najwa S. Hirn. All rights reserved.