Thread: How to solve this problem algebraically?

Qs: One number is 6 more than another. Their product is 520. Find the numbers.

-- Let the numbers be: x, x+6
So, x(x+6) = 520
or, x^2+6x=520
then what..?

The numbers are 20 & 26.
And if I put them in the above formula, it works..
20(20+6) = 520
or, 20x26=520

Are you aware of any of the methods available for solving a quadratic equation?

One number is 6 more than another. Their product is 520. Find the numbers.

Let any letter of choice be the number we are searching for. I will use n for number but you can use x, y, z, or whatever letter you like.


Let n = one of the numbers

Let n + 6 = the other number


The words "Their product" should tell you right away that multiplication is what the question is leading to.

n times (n + 6) = 250


n(n + 6) = 250


n^2 + 6n -250 = 0


We have a quadratic equation.


Use the quadratic formula.


In the quadratic formula, let a = 1, b = 6 and c = -250.


See link below to learn about this famous formula.

The Quadratic Formula Explained

If after visiting the site you have no clue what's going on, write back. I think it is important for you to try this one on your own. Keep in mind that x is typically used in the formula. Just replace my letter n with the typical variable x and follow the steps given in the link above.

Thanks for Both of the above posts. I've solved it using the factoring method e.g.
factors of 520 that will match to x, x+6 are 20 & 26
Since, x^2 + 6x -520 = 0
(-20)(26) = -520
(-20)+(26)= 6
So, (x-20)(x+26)=0
x-20 = 0, or x=20
x+26 = 0, or x=-26
x=20 ... this matches the equation, so the #s are 20 & 26.
Will try the formula way also. Thanks again...