+0  
 
0
51
1
avatar

Five times the second of three consecutive even integers is six more than twice the sum of the first and third integer. Find the middle even integer.

 Jan 24, 2020
 #1
avatar+24133 
+2

Five times the second of three consecutive even integers is six more than twice the sum of the first and third integer.

Find the middle even integer.

 

I assume:

\(\text{Let the first even integer $=2(n-1)$ } \\ \text{Let the middle even integer $=2n$ } \\ \text{Let the third even integer $=2(n+1)$ }\)

 

\(\begin{array}{|rcll|} \hline 5(2n) &=& 6+2\Big( 2(n-1)+2(n+1) \Big) \\ 10n &=& 6+2( 2n-2+2n+2 ) \\ 10n &=& 6+2*4n \\ 10n &=& 6+8n \\ 10n-8n &=& 6 \\ \mathbf{2n} &=& \mathbf{6} \\ \hline \end{array}\)

 

The middle even integer is 6

 

laugh

 Jan 24, 2020

13 Online Users

avatar