0

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!

J. M. ain't a mathematician
  • 75,051
Gabriel Panduro Jr
  • 13
  • If Chris spied $270$ and Kelly spied $540$, then Kelly would have actually spied $100%$ more (of an amount that Chris spied) than Chris did, not $50%$. When talking about percentages, it is imperative to keep track of what the percentages are of. – JMoravitz Mar 28 '18 at 19:28
  • Although, if Chris spied $270$ and Kelly spied $540$, then Kelly would have spied $50%$ more of an amount that Kelly spied than Chris did, this is not how the sentence is generally interpreted when the clarification of what the percentage is of is omitted. – JMoravitz Mar 28 '18 at 19:34
  • @JMoravitz Post this as the answer. Yes, it's elementary, but it's what the OP needs. – Ethan Bolker Mar 28 '18 at 23:49
  • Thank you so much! Much appreciated :) lots of help everyone. I hate word problems:/ I always have difficulty interpreting them. – Gabriel Panduro Jr Mar 29 '18 at 00:55

3 Answers3

0

Using ratios

$540 : 150\%$

$x : 100\%$ (True number)

Drawing an X yields

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

F.A.
  • 1,001
Aladdin
  • 58
  • 5
0

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.

Dylan Zammit
  • 1,218
0

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:

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

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

it's a hire car baby
  • 9,243