What is the algebra equation and how to translate words into algebra equation?

Using an equal sign to express the equal relation of two algebra expressions is called the equation.

Example 1:

The words expression is : If the width of a rectangle is twice the length of the rectangle, find its area.

Solution:

Let x be the length of the rectangle, then its width is 2x,

The equation is : The area of the rectangle = x ( 2x ), that is, Area of the rectangle = 2x²

Note: The area of a rectangle is the product of its length and width.

Example 2:

The words expression is: The sum of three consecutive integers is 24, what are the three integers?

Solution:

Let x, x + 1, and x + 2 be the three consecutive integers. Since the sum of the three consecutive integers is 24

The equation is : x + x + 1 + x + 2 = 24 -> 3x + 3 = 24 -> 3x = 24 - 3 -> 3x = 21 -> x = 7

The three integers are 7, 8 , 9.

Note: the word 'is' represent an equal relation.

Example 3:

The words expression is: Alice is eleven years order than her brother John. Three years ago, the sum of their ages was 21 years. How old are Alice and John now?

Solution:

Let A be Alice and J be John. Since Alice is 11 years older than her brother John, then the equation is A = J + 11

Three years ago, the age of Alice was A - 3, the age of John was J - 3. Since three years ago, the sum of their ages was 21 years, the age equation was:

A - 3 + J - 3 = 21 -> A + J - 6 = 21 -> A + J = 21 + 6 -> A + J = 27

Substitute equation A = J + 11 into the equation A + J = 27

J + 11 + J = 27 -> J + J = 27 - 11 -> 2J = 16 -> J = 8, A = J + 11 = 8 + 11 = 19

Therefore, Alice is 19 years old and John is 8 years old now.