Question

How do you find three consecutive even integers such that the sum of twice the first and third is 40?

Answer 1

Hint: As we know sum is result of adding two or more numbers and difference is result of subtracting two or more numbers and hence, here we need to find three consecutive even integers such that the sum of twice the first and third is, hence for this consider any random variable as ‘x’ and form the equations as per the given statements in the question and then evaluate the terms to get the value of the x.

Complete step by step solution:
For any given unknown term in the question, we need to consider any random variables for the unknown term.
As mentioned in the question the three consecutive even integers such that the sum of twice the first and third is 40 i.e.,
The three consecutive even integers are:
\[x,x + 2,x + 4\]
Twice the first means \[2x\] and third is \[x + 4\].
Next, as given we need to sum them equal to 40 as:
\[ \Rightarrow 2x + \left( {x + 4} \right) = 40\] …………………….. 1
\[ \Rightarrow 2x + x + 4 = 40\]
Now, evaluate the terms, we get:
\[ \Rightarrow 3x + 4 = 40\]
\[ \Rightarrow 3x = 40 - 4\]
Simplify the terms, to get the value of x as:
\[ \Rightarrow 3x = 36\]
\[ \Rightarrow x = \dfrac{{36}}{3}\]
Hence, we get:
\[ \Rightarrow x = 12\]
The three consecutive even integers are: \[x,x + 2,x + 4\] i.e.,
Our first even integer is: \[x = 12\]
The, second even integer is \[x + 2\], hence substituting the value of x we get:
\[x + 2 = 12 + 2 = 14\]
Now, third even integer is \[x + 4\], hence substituting the value of x we get:
\[x + 4 = 12 + 4 = 16\]
Hence, the three consecutive even integers are: 12, 14 and 16.
As given, sum of three consecutive even integers such that the sum of twice the first and third is 40, hence we have from equation 1 as; \[2x\] and \[x + 4\], evaluating this we get:
\[ \Rightarrow 2x + \left( {x + 4} \right) = 2\left( {12} \right) + \left( {12 + 4} \right)\]
Simplifying, the terms we get:
\[ \Rightarrow 2x + x + 4 = 24 + 16\]
\[ \Rightarrow 2x + x + 4 = 40\]
Therefore, the sum of three consecutive even integers is 40.

Note: To find any values for these types of statements we need to consider any random variables as the unknown term, next solving as per the statements stated we can find out the values of any number asked. If they are asked to find three numbers then consider \[x,y,z\]as the unknown variables and solve the given question.