julietmarie7
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Find four consecutive even integers such that the sum of the second and fourth and integer is one half times the sum of the first and third integers

Respuesta :

KatsuekiX
Okay lets create an eqn from that information

A first int, B second int, C third int, D fourth int.

B = A + 2
C = A + 4
D = A + 6
A is the smallest integer

B + D = 0.5 (A + C) 

Now lets substitute

(A + 2) + (A + 6) = 0.5(A + (A + 4))
now lets dist

2a + 8 = 0.5(2a +4)
2a + 8 = a + 2
a + 8 = 2
a = -6

B = -6 +2
B = -4
C = -6 + 4
C = -2
D = -6 + 6
D = 0

Now using B + D = 0.5(A + C)
-4 + 0 = 0.5(-6 + (-2))
-4 = 0.5 (-8)
-4 = -4

Correct 
Therefore, First integer is -6, second integer is -4, third integer is -2 and fourth integer is 0

The value of four consecutive even integers such that the sum of the second and fourth and integer is one half times the sum of the first and third integers is -6,-4,-2,0.

What is an algebraic expression?

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression is used to represent the general problem in the mathematical way to solve them.

Let the smallest term of the four consecutive even integers is a. Thus, the second, third and fourth term will be,

[tex]\text{2nd}=a+2\\\text{3rd}=a+4\\\text{4th}=a+6[/tex]

The sum of the second and fourth and integer is one half times the sum of the first and third integers. Thus,

[tex](a+2)+(a+6)=[(a)+(a+4)]\times \dfrac{1}{2}\\2a+8=(2a+4) \dfrac{1}{2}\\4a+16=2a+4\\4a-2a=4 -16\\2a=-12\\a=-6[/tex]

Thus, the value of four consecutive even integers such that the sum of the second and fourth and integer is one half times the sum of the first and third integers is -6,-4,-2,0.

Learn more about the algebraic expression here;

https://brainly.com/question/2164351

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