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 (the smaller integer) and (the larger integer).
According to the problem, the larger integer is 10 more than 4 times the smaller integer. This gives us the equation:
Now, solve for :
Subtract from both sides:
Now, subtract 10 from both sides:
Now, divide both sides by 3:
So the smaller integer is , and the larger integer is:
Thus, the two consecutive integers are and .
Would you like further explanation or details on this? Here are some related questions:
- How would the equation change if the larger integer were 5 more than 3 times the smaller?
- What if the difference between the two integers was given instead?
- Can you solve for integers where the larger is a fraction more than the smaller?
- How does the problem change if the integers are not consecutive?
- What are other methods to check the solution?
Tip: For consecutive integers, always set up variables in terms of and .
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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
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