Math Problem Statement

The sum of two consecutive numbers is -161. Find the value of the greater number.

Solution

Let the two consecutive numbers be represented as xx and x+1x + 1, where xx is the smaller number. According to the problem, the sum of these two numbers is -161. We can express this as the following equation:

x+(x+1)=161x + (x + 1) = -161

Simplifying the equation:

2x+1=1612x + 1 = -161

Now, subtract 1 from both sides:

2x=1622x = -162

Divide both sides by 2:

x=81x = -81

Since xx is the smaller number, the greater number is:

x+1=81+1=80x + 1 = -81 + 1 = -80

Thus, the value of the greater number is 80\boxed{-80}.

Would you like any additional explanation on this?

Related questions:

  1. What is the sum of two consecutive even numbers if their sum is 120?
  2. How do you find two consecutive odd numbers whose sum is 100?
  3. What is the equation for the sum of two consecutive numbers if their sum is xx?
  4. How does this method change if the sum of three consecutive numbers is given?
  5. Can you find three consecutive even numbers whose sum is 180?

Tip: When dealing with consecutive numbers, always set one as xx and express the next as x+1x+1, x+2x+2, etc.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

x + (x + 1) = -161
2x + 1 = -161

Theorems

Properties of consecutive integers
Solving linear equations

Suitable Grade Level

Grades 6-8