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Challenge yourself with a math problem: three even numbers add up to 108. Determine the largest number in this puzzle and test your math skills!
The sum of Three Consecutive even Integers is 108. What is the Largest Number?
The Largest number is 38.
Explanation
Let’s call the first number in the sequence “x”.
Since the integers are consecutive and even, the next integer in the sequence would be x + 2, and the one after that would be x + 4.
We know that the sum of these three integers is 108, so we can set up an equation:
x + (x + 2) + (x + 4) = 108
Combining like terms, we get:
3x + 6 = 108
Subtracting 6 from both sides, we get:
3x = 102
Dividing both sides by 3, we find:
x = 34
Therefore, the first number in the sequence is 34.
The largest number in the sequence is x + 4, which is:
34 + 4 = 38
So, the largest number in the sequence is 38.
Solving Linear Equations in Algebra
A linear equation is an equation where the highest power of any variable is 1. Solving a linear equation means finding the values of the variables that make the equation true. For example, if you have the equation 2x + 3 = 7, solving it means finding the value of x that makes the left side equal to the right side (in this case, x = 2).
There are different methods for solving linear equations, depending on the complexity of the equation and the number of variables involved. Here are some common methods:
1. Single-variable equations:
- Isolating the variable: This involves manipulating the equation to get the variable by itself on one side, and a constant on the other side. For example, in the equation 2x + 3 = 7, subtracting 3 from both sides and then dividing both sides by 2 would isolate x, giving you x = 2.
- Combining like terms: This involves grouping and combining similar terms on both sides of the equation. For example, in the equation 3x + 2y = 5x – y, combining the x terms and the y terms would give you 2x + y = 5.
- Substitution: If you have two equations with two variables, you can solve for one variable in terms of the other in one equation, and then substitute that expression into the other equation to solve for the other variable.
2. Systems of linear equations:
- Graphing: This involves plotting each equation as a line on a coordinate plane. The solution is the point where the two lines intersect.
- Elimination: This involves manipulating the equations to eliminate one of the variables, and then solving for the remaining variable. This can be done by adding or subtracting the equations together when the coefficients of one of the variables have opposite signs.
- Matrices: This method involves converting the system of equations into a matrix and then using matrix operations to solve for the variables. This is typically used for more complex systems with multiple variables.
No matter which method you use, the goal is always the same: to find the values of the variables that make the equation true.
Here are some additional things to keep in mind:
- It is important to check your answer by plugging it back into the original equation to make sure it makes the equation true.
- There may be multiple solutions to a system of linear equations, or there may be no solutions at all.
- There are many online resources and tools available to help you solve linear equations.
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