Question

A number Y is chosen at random from the set of all prime numbers less than 50. If hundred
more than one-fifth the square of Y is less than nine times Y. Find the value of Y.

A) 23
b) 31
C) 29
D) Can not be determined

Answer 1

Hey :)

Answer 2

A hunder more than 1/5 the square of Y,
let's write that out,

\(\rm \frac{1}{5}Y^2+100\)

Answer 3

is less than 9 times Y,\[\large\rm \frac{1}{5}Y^2+100<9Y\]

Answer 4

Multiply by 5,\[\large\rm Y^2+500<45Y\]Subtract everything to the left,\[\large\rm Y^2-45Y+500<0\]

Answer 5

Then what can we do from there :d
Hmm thinking..

Answer 6

Y = 20 or 25.

Hence, answer would be 23.

Thank you @zepdrix :)

Answer 7

It turns out that this factors nicely,\[\large\rm (Y-25)(Y-20)<0\]

You figure it out? Yay good job c: