Question

PLEASE HELP! A positive number is 1/3 of another number. The sum of the numbers is five less than the square of the larger number. Find the numbers. PLEASE SHOW WORK Thanks!

Answer 1

Answer: The numbers are 1 and 3.

Explanation:

Let x = smaller number , y= larger number.

As per given,

`x=(y)/(3)` ...(i)

`x+y=y^2-5` ...(ii)

Put value of x from (i) in (ii)

`(y)/(3)+y=y^2-5\\\\\Rightarrow\ \frac43y=y^2-5\\\\\Rightarrow\ 3y^2-4y-15=0\\\\\Rightarrow\ 3y^2-9y+5y-15=0\\\\\Rightarrow\ 3y(y-3)+5(y-3)=0\\\\\Rightarrow\ (y-3)(3y+5)=0\\\\\Rightarrow\ y=3 \ \ or\ y=(-5)/(3)`

Since numbers are positive , so y=3 is correct.

And x will be 1 [from (i)]

Hence, the numbers are 1 and 3.