Word Problem

Question

the sum of two numbers is 210. If one number is the square of the other, find the set of numbers

Answer 1

Okay, this one you can read right off.

 

The sum of two numbers is 210.

 

A + B = 210

 

One number is the square of the other

 

A = B²

 

What are the numbers?

 

Okay, substitute B2 into the first and solve

 

B² + B = 210

 

B(B+1) = 210

 

This equation leaves two easy ways to find the numbers. 

 

Either take the square root of 20, and round down for B, or take the prime factors of 210, and make two consecutive numbers out of them, the lowest being B.

 

The square root of 210 is about 14.5; The prime roots of 210 are 2, 3, 5 and 7; Either way, the answer for B is 14, and A must then be B², which is 196.

 

 

Answer 2

Let one number be x

Then other number must be x²

 

Now x² + x = 210

 

Solve this quadratic equation

 

x² + x - 210 = 0

 

x² + 15x - 14x - 210 = 0

 

x(x + 15) - 14(x+15) = 0

 

(x-14)(x+15) = 0

 x = 14 or x = -15

 

one number can be 14 and other number 196

 

or

one number can be -15 and other number 225

:)