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.

Step-by-step explanation:

Let x = smaller number , y= larger number.

As per given,

$x=\dfrac{y}{3}$   ...(i)

$x+y=y^2-5$       ...(ii)

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

$\dfrac{y}{3}+y=y^2-5\\\\\Rightarrow\ \dfrac43y=y^2-5\\\\\Rightarrow\ 3y^2-4y-15=0\\\\\Rightarrow\ 3y^2-9y+5y-15=0\\\\\Rightarrow\ 3y(y-3)+5(y-3)=0\\\\\Rightarrow\ (y-3)(3y+5)=0\\\\\Rightarrow\ y=3 \ \ or\ y=\dfrac{-5}{3}$

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

And x will be 1  [from (i)]

Hence, the numbers are 1 and 3.