SLC- S22W1: "Variables and Expressions"

Hello friends and welcome to my article in the SLC: S22/W1 and I duly appreciate @khursheedanwar for the graceful thought of incorporate logic arithemtic into this great lessons. I love arithemtic and remain more than ready to share my thoughts on this great conquest.

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TASK 1: Explain two variables and expression types other than that which are explained in this course.

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Continuous Variables:
These can also be known as quantitative variables, they are specially used in groups observation, dividing data into indistinct groups and categories, which lack countable values. Examples; gender, marital status
^link🔗

Continuous Variables:
Continuous Variables are quantitative variables that take number of valued within a range. The variables are measured along a continuum, representing very precise measurement. Good example is height, temperature, time.

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TASK 2: Show your way of evaluating an algebraic expression if values of variables are given? Step by Step explanation required

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An algebraic expression can be evaluated easily in simple ways. I would be showing guides on how to evaluate an algebraic expression. But firstly a background note must be made on algebraic expression.

Algebraic expression must eventually involve a variable, constant and one or more mathematical expressions. Importantly, it mustn't be equated to another value. Once an expression gets equated through an = it turns from an expression to an equation

Example: 50x + 45 - 20x is an algebraic expression due to the fact that it contains variables x special constants 50, 45 and 20. Mathematical operation which are + and - respectively.

Example of an algebraic equation would be 50x + 45 = 30 - 4x Once there is an = sign which comes to play it turns to an equation. From this the variables are xcoefficients are 50, 45, 30 and 4 respectively, mathematical operations + - =

Evaluating an algebraic expression would require using the PEMDAS expression technique which explains the basic approach. PEMDAS according to the lesson means Parentheses, Exponents, Multiplication, Division , Addition and Subtraction respectively As shared in the class

Lets imagine an algebraic operation
42 + 8 - 2 ÷(2×4)(5-3)

We firstly analyse the expressions in the parenthesis following the lesson guide, (2×4)=8 for first parenthesis and (5-3)=2
We multiply (8)(2) which gives us 16 We go further to analyze the other figures which are 42 + 8 -2 which gives 50-2 which is 48 We further divide 48÷16=3 therefore our final answer is 3

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^{TASK 3: This is an expression x-2 where x=5 , evaluate it! Make the following expression simplified 8(x+3)+1
Simplify this expression: 3(2x - 1) + 2(x + 4) - 5
Evaluate this expression: (x^2 + 2x - 3) / (x + 1) when x = 2
Solve the following equation: 2x + 5 = 3(x - 2) + 1}

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Solving the equation respectively in the screenshot below.

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TASK 4: Suppose bakery sells total of 250 loaves of bread per day, Selling while 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 after bakery is making a profit of $0.50 for each white bread loaf and $0.75 for each whole loaf then please write expression for representing bakery total daily profits

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We firstly define our parameters accordingly;
x represent assumed white bread loaf
30x represent assumed number of wheat

Therefore x+30x = 250

Simplifying for x we have...

31x = 250

Dividing both expressions by 31 to make x the subject we have;

x = 8.06

To check if we are correct we substitute 8.06 into the equation.

x+30x = 250

Substituting we have

8.06 + 30(8.06) = 250
8.06 + 241.8 = 249.86 approximately 250!

Profit margin determination is this;
0.50x + 0.75(x+30)
0.50(8.06) + 0.75(8.06+30) simplifying
4 + 38.81
Profit daily = $42.81

Scenario 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.}

Total Cost = (2x +15)
Mentioned package = (3x-2)
number of hours = x
exceeded number of hours = 4+x

(2x+15)+(3x-2)=4+x

Simplifying
(2x + 15)+(3x-2)=4+x
2x+3x+15-2=4+x
5x-x= 4-15+2-3
4x= 12
Dividing both sides by 4
x= 3 hours

This is the mathematical representation of the word problem given and thus an algebraic expression for the tasked asked above.

I invite @sahmie @josepha @dove11 @eliany to join challenge