133k views
1 vote
Please help my little sis!

The product of two whole numbers is 14391 and their difference is 6. What are the two numbers?

User Sonita
by
3.4k points

2 Answers

6 votes

Answer:

117 and 123.

Explanation:

If the 2 numbers are x and y we have the system of equations:

x - y = 6

xy = 14391

From the first equation y = X - 6 so substituting:

x(x - 6) = 14391

x^2 - 6x= 14391

x^2 - 6x - 14391 = 0

The prime factors of -13491 are -3*3*3*13*41

Now 3*3*13 = 117 and -3 * 41 = -123,

so the factors are:

(x - 123)(x + 117) = 0.

x = 123, -117.

As x is a whole number we take the positive value 123.

So x = 123 and y = 123 - 6 = 117.

User Dvtoever
by
3.9k points
4 votes
I would put this in an algebraic equation:
First whole number is x
Second whole number is x + 6
So try and solve x(x+6)=14391

My next step, after I put this down would be to rearrange it into a solvable quadratic

X^2 + 6X - 14391 = 0

Using the quadratic formula (below)

Please help my little sis! The product of two whole numbers is 14391 and their difference-example-1
User Kadeshpa
by
3.4k points