# Algebra in Everyday Life

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.

## Examples of using algebra in everyday life

Here are some simple examples that demonstrate the relevance of algebra in the real world.

## Going shopping

You purchased 10 items from a shopping plaza, and now you need plastic bags to carry them home. If each bag can hold only 3 items, how many plastic bags you will need to accommodate 10 items?

#### Explanation :

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.

## Calculating grocery expense

#### Explanation :

The figure below shows the three items in different shapes and colors.

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

## Filling up the gas tank

You need to fill the gas tank but you have only $15 in your pocket. If the price of the gas is$3 a gallon, how many gallons can you buy?

#### Explanation :

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

#### Explanation :

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

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.

## The area of a rectangle is 72cm^2, in which the width is twice its length. What is the dimension of the rectangle?

#### Explanation :

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

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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