"SLC-S22W1/Variables and Expressions"

It feels great to see a mathematics being taught here. This is really good as many people have issues understanding mathematics. Great thanks to @khursheedanwar, for making this possible.

So Iet me start, we are learning about variables this week.

• Explain any two variables and expressions types other than that which are explained in this course.(Practical and algebric examples are required!)

Variables are algebraic symbols which are used to represent data which can be changed, altered and increased.

This data is not static like constants and can assume any figure depending on what is required.

Any alphabet can be used to represent variables. For example, see the expression below.

5w-4h.

In the example above, we have two variables. The variables are w and h

Variables can be stated in the form an expressions to enable the user understand the meaning and application of the variables.

We have two types of variables: independent variable and dependent variable. Now let me explain these two.

Dependent variable - This is the type.of variable which is usually dependent on other variables or factors. Its result or outcome os clearly a function of other variables.

For example, let"s look at this expression.

w = 3 + 4h

In the example above, w is a dependent variable, because the outcome or result is dependent on the value of h
Let me go further to explain, if h in the above expression is 4, then w = 17 i.e (3+(4x4)), but if h is 2, the w = 11 i.e (3+(4x2)).

So we can see that w changes as h changes.

Now let us go independent variables

Independent Variables

These variables are not dependent on other variables for their result. Take a look at the same example I used above.

w = 3 + 4h

h in this expression is an independent variable. It can not be changed or modified when it is applied, rather what is its value determines the value of the dependent variable w

Let us use a real life example. In a bread factory, a bag of flour is used to produce 10 loaves of bread, so the quantity of bread can be determined by the number of bags of Flour used.

Let the flour be represented as w,

So the statement above can be represented as 10x..

Example 2: A firm produces a pair of shoe at a cost of $4/pair of shoe and a fixed cost of $6 each day. A pair of shoe is represented by b
So to calculate the total cost of production, it will be shown as follows -

*Total cost (w) = 4b + 6

In the expression above, w is a dependent variable while b is an independent variable. The value of b determines what w will be.

Show your way of evaluating of an algebraic expression if values of variables are given? Step by step explanation required!

(The more you will be detailed and accurate,the more your task will be perfect!)

First, solving an algebraic expression requires following a systematic method to get an answer. This systematic method as the PEMDAS method. So this shows the order by which a problem is to be solved.

The order of solving it goes this way:

° P -first, solve the ones in parenthesis or brackets.

° E - followed by the ones that have exponentials

° M - next are the ones that we need to multiply.

° D - division follow next.

° A - Addition comes next and finally

° S - Subtraction. If we don't follow this order, we would not get the right answer to the problem.

Let us now solve this expression

3x + 10 = 2(x+10)

Always remember our systematic order of solving it.
First, we solve the ones in bracket 2(x+ 10),
This will them be 2x+20

Thus our new equation will become

3x + 10 = 2x + 20

We then collect the like terms together: Isolating the variable.

3x -2x = 20x - 10x. (Subtraction of the like terms now takes place)

X = 10

Task 3

(1) Simplify this expression: 3(2x - 1) + 2(x + 4) - 5

(2) Evaluate this expression: (x^2 + 2x - 3) / (x + 1) when x = 2

(3) Solve the following equation: 2x + 5 = 3(x - 2) + 1

Task 4(1)

Suppose there's a bakery selling a total of 250 loaves of bread per day. They are selling whole wheat and white bread loaves with numbers of whole wheat loaves sold being 30 more than the number of white bread loaves. If x is representing number of white bread loaves sold out and bakery is making a profit of $0.50 for each white bread loaf and $0.75 for each whole wheat loaf then please write an expression for representing bakery total daily profit.

######### Solution

Let the number of white bread sold be represented by = w

The quantity off whole wheat bread sold = w+30, (this is because it is sold 30 more than the white bread)

Total loves sold = 250

Having these data, we will use this equation to represent the number of bread sold.

w + (w + 30) = 250

I will collect the like terms together

w + w + 30 = 250

2w = 250 - 30

2w = 220

Therefore

w = 220/2

w = 110

We have now seen that the quantity of white bread sold is 110 loaves = w.

To now calculate the quantity of whole wheat bread sold, we will now place 110 for w in the original expression for Whole wheat bread.

W + 30 = 110 + 30 = 140

Whole wheat bread sold is now = 140

We will now calculate the total daily profits

The profit accruing from sales of white bread loaves = $0.50 * w = $0.50 * 110 = $55

The profit accruing from whole wheat loaves = $0.75* (w + 30) = $0.75 * 140 = $105

Therefore, the total daily profi will be

Profit from white bread +profit from whole wheat bread

Total profit = $55 + $105

Total profit = $160

To reconfirm the answer, let is substitute the values of w( white bread) and w+30(whole wheat bread)

Total daily profit = $0.5 x 110 + $0.75 x 140
= $55 + $105
= $160

So the expression for representing the bakery"s daily total profit is

Total daily profit = $0.5(w) + $0.75(w+30)

Task 4 (2)

Suppose that cost of renting a car for a day is re-presented by the expression 2x + 15 and here x is the number of hours in which car is rented. If the rental company offers a package of 3x - 2 dollars for customers who take car at rent for more than 4 hours then write an expression for the total cost of renting the car for x hours and show how you simplify it.
The expression showing the total cost of renting a car will be:

Total cost = (2x + 15) - (3x - 2).

To simplify it further,

Total cost = (2x+15) - (3x-2)
= 2x+15-3x+2
Then collect like terms together

                 =2x-3x +15+2

Total cost = -x+17

Once more, thank you
@khursheedanwar for this wonderful opportunity.