Answer :
You have to find 4 consecutive integers whose sum is 270.
Let "x" represent the first integer.
The next one can be expressed as (x+1)
The third one can be expressed as (x+2)
The fourth one can be expressed as (x+3)
The sum of these integers must be 270 so that:
[tex]x+(x+1)+(x+2)+(x+3)=270[/tex]From this expression, you can determine the value of x:
- First, order the like terms together and simplify:
[tex]\begin{gathered} x+(x+1)+(x+2)+(x+3)=270 \\ x+x+1+x+2+x+3=270 \\ x+x+x+x+1+2+3=270 \\ 4x+6=270 \end{gathered}[/tex]-Second, subtract 6 to both sides of the equal sign to pass the term to the right side of the expression:
[tex]\begin{gathered} 4x+6-6=270-6 \\ 4x=264 \end{gathered}[/tex]-Third, divide both sides by 4 to determine the value of x:
[tex]\begin{gathered} \frac{4x}{4}=\frac{264}{4} \\ x=66 \end{gathered}[/tex]Now that you know the value of the first integer, you can determine the other three:
[tex]\begin{gathered} x=66 \\ x+1=66+1=67 \\ x+2=66+2=68 \\ x+3=66+3=69 \end{gathered}[/tex]The four consecutive integers that sum 270 are 66, 67, 68, and 69. (option b)
