Question

solve
The sum of three consecutive even integers is 270. find the integers.

Answer 1

Step-by-step explanation:

We will let x be the first of our three consecutive even integers. Since x is even, we know that the next integer, which can be found by adding 1 to x, is an odd number. The integer after that would then be odd, meaning that the second of our consecutive even integers is found by adding 2 to x. Similarly, the third of our consecutive even integers is found by adding 2 to the second even integer.

So, with x be the first of our three consecutive even integers, we get that our three numbers are x,x+2, and (x+2)+2x,x+2, and (x+2)+2.

Now, we are given that the sum of these three consecutive even integers is 270, giving us the equation below:

x+x+2+x+2+2=270x+x+2+x+2+2=270

We can then solve this equation with one variable as shown below:

x+x+2+x+2+2=270⇒3x+6=270⇒3x+6−(6)=270−(6)⇒3x=264

$= > \frac{3x}{3} = \frac{264}{3}$

⇒x=88x+x+2+x+2+2=270⇒3x+6=270⇒3x+6−(6)=270−(6)⇒3x=264⇒3x3=2643⇒x=88

Since x=88x=88, we get that our three consecutive even integers are 88,90, and 9288,90, and 92. The biggest of these is 9292, which is our answer!

Answer 2

SoluTion :-

Let the 1st number be x

2nd number = x + 2

3rd number = x + 2 + 2

According to the question

$\rm {x+(x+2)+(x+2+2)=270}\\\\\\\rm {3x+6=270}\\\\\\\rm {3x=270-3}\\\\\\\rm {3x=264}\\\\\\\rm {x=\frac{264}{3}}\\\\\\\rm {x=88}$

Thus,

1st number = 88

2nd number = 88 + 2 = 90

3rd number = 88 + 2 + 2 = 92

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Verification :-

$\rm {88 + (88 + 2) + (88 + 2 + 2) = 270}\\\\\\\rm {88 + 90 + 92 = 270}\\\\\\\rm {270 = 270}$