find two consecutive even positive integers whose product is 624

Question

find two consecutive even positive integers whose product is 624

Answer 1

Hi Ilse, Let x=first even number then x+2 would be the next even number. (x)(x+2)=624. x^2 +2x=624. x^2 +2x -624=0. Factor or use the quadratic formula. (x+26)(x-24)=0 x=-26 or x=24 We want the positive solution so x=24 and x+2=26 24*26=624 so it works.

Answer 2

Hello llse,

First you need to define your variables.  Think of what consecutive even numbers would be......

2, 4, 6,.....      10,12,14,16....   Etc.

what if I started with x?

well it takes +2 to get to the next number, so the variables I need are:

x: the first positive even integer

x+2 : the second positive integer

 

Secondly, I need to "interpret" the English word product to the math operation MULTIPLICATION.

this means my equation is

x(x+2) =624

x^2 +2x =624  distribute the x to both factors in the parentheses

x^2 +2x -624=624-624. Move all parts to one side of the equation

x^2 +2x -624=0. Simplify, now factor because it is a squared equation

(x-24)(x+26)=0 two numbers that equal 624when multiplied but 2 when added together 

x-24=0. And x+26=0.  Set each factor equal to zero and solve

x=24.       And x=-26. Simplify

x+2=26.   and x+2=-24. Finding the second even integer

But wait, the problem wants POSITIVE even integers so 2 of the solutions DO NOT work (-26,-24, they are negative) be careful sometimes you get extraneous ("extra") solutions, look at your defined variables.

the solutions we want are 24 and 26. 

 

Answer 3

Let the first consecutive even positive integer be x

That means that the next positive even integer will be x + 2

 

now the product (multiply them) will look like this:

 

x(x +2)

 

that equals 624

 

so,

 

x(x + 2) = 624

 

x² + 2x = 624  

 

set the equation equal to zero by subtracting 624 from both sides

 

x² +2x - 624 = 0

 

factor

 

(x - 24)(x + 26) = 0

 

Thus x = 24   OR x = -26

 

But we must use the 24 because of what the original problem says "even positive integers"

 

So the next consecutive even positive integer will be 24 + 2 which is 26

 

Now check:

 

24 times 26 IS 624

 

Bill

Answer 4

Hey Ilse -- since the numbers are "next to each other," a square root can start us ...

625 = 25 x 25 ==> 24 x 26 will do it ... Best regards :)