Simple Elementary algebra

Question

Kelly peeked around the corner and spied $540$ of them not studying. If this was $50\%$ more than Chris spied, how many did Chris spy?

My answer was $270$ and marked incorrect. Why?

Please help explain. Thank you!

Answer 1

Using ratios

$540 : 150\%$

$x : 100\%$ (True number)

Drawing an X yields

$\dfrac{540\cdot100}{150} = 360$

Answer 2

Say Chris has spied on $x$ people, "50% more than x is 540" translates to: $$\dfrac{150}{100}\cdot x = 540$$Get $x$ as subject of the formula and you get your answer.

Answer 3

You've worked out as if Kelly spied 100% more than Chris spied. 50% more isn't double. It's half as much again.

You want:

$540=\frac{150}{100}\times C$

$C=540\times \frac{2}{3}=360$