Algebra Word Problem: Setting up Problem (Spanish & English)

A total of r players came to a basketball practice.  The coach divides them into four groups of t players each, but two players are left over.  Which expression shows the relationship between the number of players out for basketball and the number of players in each group?

La suma de jugadores viene a la práctica para basquetbol y está representado con r.   El entrenador les divide a los jugadores en cuatro grupos. La suma de jugadores en cada grupito está representado con t.  Sin embargo, dos de los jugadores no están en un grupito. ¿Cuál expresión muestra la relación entre la suma de jugadores a la práctica y el número de jugadores en cada grupito?

a.        (t +4) -2 = r

b.      4t – 2 = r

c.       4t + 2 = r

d.       4t/2 = r

 

Answer:  C

Algebra Word Problem: Body Mass Index (Spanish & English)

 

Body Mass Index (BMI) can be defined as BMI =  (705)(w)/ (height squared)  where w is a person’s weight in pounds and h is the person’s height in inches.  If Cody is 65 inches tall and weighs 125 pounds, what is his body mass index?  Round to the nearest whole number.



Índice de Masa Corporal está definido como Índice de Masa Corporal = (705)(w)/ (height squared)   donde w es la pesa de una persona y en las libras y h es la altura de la persona en las pulgadas.  Si Cody tuviera 65 pulgadas de altura y pesara 125 libras, ¿Qué estaría su Índice de Masa Corporal? Redondear hasta la más cerca numero entero.



Answer:  21

Dividing Integers- Positive and Negative Numbers

Learning and practicing the "how to" of dividing integers and be difficult.  This link provides access to many dividing integers worksheets just like the one below.

Mean is the average of a group of numbers. To find the mean of a group of numbers you first add all the numbers together. You then divide by the number of elements you have in the data set. Let's try an example. Data set: 3, 5, 9, 8, 10 Number of elements: 5 Mean = (3 + 5 +9 + 8 + 10)/5 = 7 Now you can try an example. Data set: 6, 7, 8 11, 15, 7, 23 What is the data set? How many elements? What is the mean? Answer coming shortly.

GED Math: Simplifying Algebra Expressions Disributive Property

I have found that one of the most difficult math concepts for GED students to understand and grasp is the concept of combining like terms, expecially those involving the Disributive Property.

I am beginning to understand that unless the learner has an almost perfect understanding of adding, subtracting, multiplying, and dividing integers (positive & negative), the process of simplifying expressions, along with the Distributive Property, is very difficult.

Students also need to have their basic math facts memorized. Many will come in understanding and knowing the basic facts of adding and subtracting. But when asked to multiply and divide.... that can be more challenging. Have them practice their facts, outside of class, using worksheets.

Even with a good grasp of integers and basic math facts, most students will need to take the concepts of the distributive property, combining like terms, and solving expressions one step at a time.

One important method is to teach a "small learning concept" and then give them a LOT of practice. For example, I taught the distribute property and went through about 7 examples. I then followed up with a worksheet containing 20 more examples! Although it seems like alot, and perhaps you might think way too much..... my students want the extra practice.

Once they understand the Distributive Property, I will then proceed and teach the combining of like terms. Here again, it will take a LOT of examples..... followed by a worksheet.

The sum of three consectutive numbers is 69. What are they?

Solution: 22, 23, 24

First Integer: x
Second Integer: x + 1
Third Integer: x + 2

(x) + (x + 1) + (x + 2) = 69
3x + 3 = 69
3x + 3 - 3 = 69 - 3
3x = 66
(3x)/3 = 66/3
x = 22

Sarah picked up 3 pizzas and cut each of the pizzas into 6 equal slices. If she has five friends over and they are all equally hungry.... how many slices will each of them get? Will there be any left over?

Answer: If there are 3 pizzas cut into six slices.... this gives a total of 18 slices. Five friends plus Sarah makes 6 hungry people. Each person will get 3 slices with 0 left over. Sure hope she ordered extra large pizzas!

GED Math Algebra: Solving Equations

Solve the following equation when x = -3

x^2 + 10 - 3x + 2x =

Solution: 9 +10 - (-9) + (-6) = 22

GED Math Algebra: Evaluating equations

Evaluate the following when y = 6 and x = 2

6 - y + 3(2 + x) =

Solution: 6 - 6 + 3(2+2) = 12

Simplify the following:

(y^2)( y^3) =

Solution: (y · y)(y · y · y) = y^5

Susan went to the clothing store and bought a sweater. The sweater was originally priced at $50. What would the cost of the sweater be at 25% off and 5.5% sales tax?

Step one: Find the cost of the sweater. $50 x .75 = $37.50

Step two: Find the sales tax. $37.50 x 0.055 = $2.06

Step three: Add the cost of the sweater and sales tax together. $ 37.50 + $2.06 = $39.56

Simplify the following:

(7 + 6)(-3 + 9) - 3(2)=

Answer: 72

Evaluate the following when x= 7 and y=5.

3(x - y) + 17 =

Answer: 23

What is.....

-9 + 10 -(-5) +5 - (6)

Answer: 5

Sally is twice as old as her sister Anna, and Anna is ten years younger than her brother Sam. If Sam is 12, how old is Sally and Anna?

Answer: You must find the variable expressions; Sam: x, Anna: x-10, Sally: 2(x-10)

x=12

Sam is 12 years old.
Anna is 2 years old.
Sally is 4 years old

Samantha spent $256 to rent a car for four days. The cost of the car was the same for each day. How much was the daily cost, including a 5.5% sales tax?

Answer: $67.52

This year the Smith family has been on a very tight budget and has finally put together a monthly budget. If their monthly food bill is $550 and their annual combined income is $47, 500, what percentage of their income is set aside for food?

Answer: First, you need to find out how much the Smith family spends each year on food. $550 x 12 months equals $6600.

Next, you need to divide $6600 by $47, 500 which equals 0.13894.

Finally, convert the decimal to a percent by moving the decimal point two places to the right.

Your answer: The Smith family spends 13.89 % or about 14% of their annual income on food.

Can you find a pattern in this series of numbers? 2, 7, 17, 37

answer: To find the pattern you need to double base number and add 3.

2 plus 2 equals 4 and 4 plus 3 is 7.

Peter decided that he wanted to go to the ice cream shop so he started from home and rode his bike down First Street for 4 miles and then took a right turn and traveled due east for another 3 miles. If he was able to take a short cut and bike from home directly to the ice cream shop, how many miles less would he have ridden?

Answer: 5 miles

Fred wants to replace the carpet in his house. If his family room measures 12 ft. by 10 ft. and the hallway measures 30 ft. by 3 ft., what is the square footage of carpet that is needed?

Answer: The family room requires 120 feet squared and the hallway requires 90 feet squared. Combined Fred needs 210 feet squared.