Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

Problem Statement: Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

Solution:

Let the three consecutive odd integers are x-2, x, x+2, where x is an odd integer.

According to the problem statement, Three times the first of three consecutive odd integers is 3 more than twice the third i.e.

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

⇒ 3(x-2) = 2(x+2) + 3

⇒3x – 6 = 2x + 4 + 3

⇒3x – 6 = 2x + 7

⇒3x -2x = 7 + 6

⇒x = 13

So, the value of x is 13 i.e. the second integer.

First integer is x – 2 i.e. 13 – 2 = 11.

Third integer is x + 2 i.e. 13 + 2 = 15. 

So, 11, 13, and 15 are the three consecutive odd integers.

What is Linear Equation?

Linear equations in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+2=5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

• 4x = 8
• 5x + 10 = -20
• 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0 

Here,

• The numbers ‘a’ and ‘b’ are real.
• Neither ‘a’ nor ‘b’ are equal to zero.

Similar Questions

Problem 1: Two times the first number is equal to three times the second number and the sum of both numbers is 5. Find the numbers.

Solution:

Let the two numbers are x and y.

According to the problem statement, 

Two times the first number is equal to three times of second number i.e.

2x = 3y . . . (i)

Also, Sum of both numbers is 5 i.e.

x + y = 5 . . . (ii)

To get the numbers, we have to solve these equations i.e.

From equation (i),

2x = 3y 

⇒ x = 3y/2

Putting x = 3y/2 in equation (ii), we get

3y/2 + y = 5

⇒ (3y + 2y)/2 = 5

⇒ 3y + 2y = 5 × 2

⇒ 5y = 10

i.e. y = 10/5 i.e. 2

So, the value of y is 2 and using this the value of x is 5-y = 5-2 = 3.

Problem 2: The sum of four consecutive numbers is 18, find the numbers.

Solution: 

Let the four consecutive numbers are x, x + 1, x + 2, x + 3 respectively.

Given: Sum of four consecutive numbers is 18.

⇒ x + x + 1 + x + 2 + x + 3 = 18 

⇒ 4x + 6 = 18 

⇒ 4x = 18-6

⇒ 4x = 12

⇒ x = 12/4

⇒ x = 3

So, the numbers should be 3, 4, 5, and 6.