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.