Word Problem

Question

The difference between two numbers is 3. If the square of the smaller number in equal to four times the larger number, find the two numbers

Answer 1

Hi Andrew

 

Interesting problem that requires 2 equations

 

You have 2 variables X and Y.

 

You know that X - Y = 3 and you know that Y² = 4X

 

If you solve the first problem for X in terms of Y it leaves you with X = 3 + Y and you can substitute that in the second equation:

 

Y² = 4(3+Y)

 

Now distribute

 

Y² = 12 + 4Y

 

then rearrange your equation to look like a standard polynomial to factor it:

 

Y² - 4Y - 12

 

factoring gives us

 

(Y+2) and (Y-6)

 

Y=6 is a great answer because it means X = 9 and 9-6 = 3 so that first equation works and 6^{2 =} 36 and 4(9) = 36 so the second equation works.

 

All the best,

 

Lori