0

# find two consecutive even positive integers whose product is 624

find two consecutive even positive integers whose product is 624

### 4 Answers by Expert Tutors

David S. | Wise Math TutorWise Math Tutor
5.0 5.0 (58 lesson ratings) (58)
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.

Michelle P. | Patient, Creative, Math tutor ready to help!Patient, Creative, Math tutor ready to h...
5.0 5.0 (129 lesson ratings) (129)
1
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.

Bill F. | Best Math Tutor in the AreaBest Math Tutor in the Area
5.0 5.0 (237 lesson ratings) (237)
1
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