The sum of two numbers is 27 and their product is 50. Find the number. Let one number be x. Then the other number is 50/x.

Question

Let one number be x. Then the other number be 50/x.

Answer 1

Right, from your fact families, one factor is equal to the product divided by the other product. 4 x 8 = 32, so 32/8 = 4 and 32/4 = 8.

 

x + 50/x = 27

 

x² + 50 = 27x

x² - 27x + 50 = 0

(x - 25)(x - 2) = 0

 

In order for the left side to equal 0, either x - 25 or x - 2 has to equal 0.

 

x - 25 = 0

x = 25

 

x - 2 = 0

x = 2

 

So, the two numbers are 25 and 2.

Answer 2

Shey,

 

Let one number be x and the other number be y.  Then we have two equations:

 

x + y = 27

x y = 50

 

So as you pointed out, y = 50/x is the other number. Now we can substitute y = 50/x into the first equation.

 

x + y = 27

becomes

x + 50/x = 27

Multiplying both sides by x gives us

x² + 50 = 27x

Subtracting 27 from both sides gives us a quadratic equation

x² -27x + 50 = 0

 

We can solve this equation by factoring:

 

(x - 25)(x - 2) = 0

 

This has two solutions 

 

x = 25 and x = 2

 

So if x = 25, then y = 2. Similarly if x = 2, then y = 25. So the numbers you are looking for are 2 and 25.  I hope this helps.

Answer 3

Ok. If one number is X and the other is 50/X:

 

X + 50/X = 27

 

X(50/X) = 50

 

X + 50/X = 27

multiply both sides by X:

X² + 50 = 27X

 

X² - 27X + 50 = 0

 

(X - 25)(X - 2) = 0

 

X = 2, 25

 

So, if X = 25, then 50/X = 2

 

or if X = 2, then 50/X = 25

 

So the numbers are 2 and 25