Find two consecutive even integers such that the sum of the larger and 3 times the smaller is 234.
I don't get how to put it as in equation.
Well, this problem can be solved using algebraic equations. Let's break it down step by step.
Let's assume the smaller even integer is x. Since we are looking for consecutive even integers, the larger even integer can be represented as x + 2.
Now, the problem states that the sum of the larger integer (x + 2) and 3 times the smaller integer (3x) is equal to 234. So, we can write the equation as:
(x + 2) + 3x = 234
Simplifying the equation, we get:
4x + 2 = 234
This equation can be further simplified by subtracting 2 from both sides:
4x = 232
Finally, dividing both sides by 4, we find the value of x:
x = 58
So, the smaller even integer is 58, and the larger consecutive even integer is 58 + 2 = 60.
Therefore, the two consecutive even integers are 58 and 60.
Let's break down the problem step-by-step to better understand how to set up an equation.
Step 1: Assign variables
Let's assume that the smaller even integer is represented by the variable "x". Since we are looking for two consecutive even integers, the larger even integer can be represented by "x + 2".
Step 2: Create an equation
According to the problem, the sum of the larger even integer (x + 2) and 3 times the smaller even integer (3x) is equal to 234. So we can set up the equation as follows:
(x + 2) + 3x = 234
Step 3: Solve the equation
Now, we can solve the equation to find the value of "x" and determine the two consecutive even integers.
x + 2 + 3x = 234
4x + 2 = 234
4x = 234 - 2
4x = 232
x = 232/4
x = 58
Step 4: Find the consecutive even integers
To find the consecutive even integers, we substitute the value of "x" back into our variable expressions:
Smaller even integer = x = 58
Larger even integer = x + 2 = 58 + 2 = 60
Therefore, the two consecutive even integers are 58 and 60.
To find two consecutive even integers, let's first assign variables to represent the integers. Let's say the smaller even integer is "x."
Since the integers are consecutive, the larger even integer will be "x + 2" because we add 2 to the smaller integer to get the next even integer.
The problem statement states that the sum of the larger integer and 3 times the smaller integer is 234.
So, we can write the equation as:
(x + 2) + 3x = 234
In this equation, we added the larger integer (x + 2) to 3 times the smaller integer (3x). The sum of these two is equal to 234.
Now, we can solve the equation to find the value of x, which represents the smaller even integer.
n and n+2
(n+2) + 3 n = 234
4 n = 232
58 and 60