We use algebra quite frequently in our everyday lives, and without even realizing it! We not only use algebra, we actually need algebra, to solve most of our problems that involves calculations.
Here are some simple examples that demonstrate the relevance of algebra in the real world.
The figure below illustrates the problem:
The different shapes inside the bags denote different items purchased. The number depicts the item number.
We use simple algebraic formula `x/y` to calculate the number of bags.
x = Number of items purchased = 10
y = Capacity of 1 bag = 3
Hence,
`10/3` = `3.33` bags ≈ `4` bags
So,we need 4 shopping bags to put 10 items.
The figure below shows the three items in different shapes and colors.
This will help your mind to calculate faster.
We will use algebra to solve the problem easily and quickly.
The prices are
a = Price of two dozen eggs = $10
b = Price of one bread = $5
c = Price of one bottle of juice= $8
=> Money needed = a + 3b + 5c
=> Money needed = $10 + 3($5) + 5($8) = $10 + $15 + $40 = $65
In the below diagram, each block represents $1, and each row is a bundle of $3, which is used to buy 1 gallon of gas.
We use simple algebraic formula,`x/y` to calculate the total gallons that can be bought.
x = Money in your pocket= $15
y = Price of 1 gallon of gas= $3
Hence,
`($15)/($3)` = 5 gallon
So, with $15 we can buy 5 gallons of gas.
Life's many problems are disguised in the form of math equations, and if we know the math, it's fairly simple to solve those problems.
1. Understand the problem
The task is to find three consecutive numbers whose total is 216.
2. Write the variable
Let "`x`" represent the first number
So, `x` = first number
`x+1` = second number
`x+2`= third number
3. Write the equation
When you add up all the numbers, you are supposed to get 216
`x + (x + 1) + (x + 2 )`= 216
`3x + 3 `= 216
4. Solve the equation
Subtract 3 from both sides
`3x + 3 - 3 `= 216 - 3
`3x ` = 213
Divide each side by 3
`(3x) / 3 `= 213 ÷ 3
`x = 71`
5. Check your answer
First number + Second number + Third number = 216
`x + (x + 1 )+ (x + 2)`
71 + (71 + 1) + (71 + 2)
71 + 72 + 73 = 216
So the three numbers whose sum is 216 are 71, 72 and 73
1. Understand the problem
A group of 5 boys goes to the theatre. The cost of ticket and popcorn is $55 and $25 respectively. What is cost per person?
2. Write the variable
Let’s say, `x` = cost of ticket/person and `y` = cost of popcorn/person
3. Write the equation
If 5 tickets cost $55, then cost of one ticket is,
`5x` = 55
`x ` = `55 / 5`
If 5 bags of popcorn cost $25, then the cost of each bag is,
`5y ` = 25
`y ` = `25 / 5`
Total cost of the movie (ticket + popcorn) per person = `x + y `
4. Solve the equation
Cost of ticket/person
`x` = `55 / 5`
`x` = $11
Cost of popcorn/person
`y ` = `25 / 5`
`y ` = $5
5. Check your answer
Cost of ticket/person + Cost of popcorn/person = Total cost
11 + 5 = 16
If we add up 16 five times (since there are 5 boys), the result is,
16 + 16 + 16 + 16 + 16 = 80
$80 is the total cost.
1. Understand the problem
The area of a rectangle is 72 cm. The width is twice its length. What is the length and width of the rectangle?
2. Write the variable
Let "`x`" be the length and "`2x`" be the width
3. Write the equation
Length `×` Width = Area
`x ` x `(2x)` = `2x^2 `= Area
4. Solve the equation
`2x^2` = Area
`2x^2` = 72
`x^2` = `72 / 2`
`x^2` = 36
`x` = 6
`x ` = Length
So, the length is 6 cm
The width is twice its length
`2x` = 2 x 6 = 12
So, the width is 12 cm
5. Check your answer
The length is 6 cm and width is 12 cm
The perimeter i.e. the distance around the edges is the sum of lengths and widths. Since rectangle has two lengths and two breadths hence the equation is,
2 x (length + width)
2 x (6 + 12) = 2 x 18 = 36 cm
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