Math Problem Statement

the larger of two consecutive integers is 10 more than 4 times the smaller find the interger

Solution

Let the two consecutive integers be xx (the smaller integer) and x+1x + 1 (the larger integer).

According to the problem, the larger integer is 10 more than 4 times the smaller integer. This gives us the equation:

x+1=4x+10x + 1 = 4x + 10

Now, solve for xx:

x+1=4x+10x + 1 = 4x + 10

Subtract xx from both sides:

1=3x+101 = 3x + 10

Now, subtract 10 from both sides:

110=3x1 - 10 = 3x

9=3x-9 = 3x

Now, divide both sides by 3:

x=3x = -3

So the smaller integer is 3-3, and the larger integer is:

x+1=3+1=2x + 1 = -3 + 1 = -2

Thus, the two consecutive integers are 3-3 and 2-2.

Would you like further explanation or details on this? Here are some related questions:

  1. How would the equation change if the larger integer were 5 more than 3 times the smaller?
  2. What if the difference between the two integers was given instead?
  3. Can you solve for integers where the larger is a fraction more than the smaller?
  4. How does the problem change if the integers are not consecutive?
  5. What are other methods to check the solution?

Tip: For consecutive integers, always set up variables in terms of xx and x+1x+1.

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Math Problem Analysis

Mathematical Concepts

Algebra
Consecutive Integers
Linear Equations

Formulas

Equation for consecutive integers: x and x+1
Linear equation solving

Theorems

Basic properties of linear equations

Suitable Grade Level

Grades 6-8