anonymous
  • anonymous
@phi
Mathematics
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
phi
  • phi
you need to use algebra. If Allen starts with x (x for unknown) marbles and doubles them, how do you write that ?
anonymous
  • anonymous
x^2?

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phi
  • phi
x^2 means x*x if you had 3 marbles, then x*x would mean 3*3 = 9 9 is not 2 times 3. any other idea ?
anonymous
  • anonymous
ugh idk
phi
  • phi
you could say: If I have x and add another x I will double how much I have x+x is one way
anonymous
  • anonymous
o yea
phi
  • phi
you can also write x+x as "I have 1 x plus another x, how many x's do I have?" 2x
anonymous
  • anonymous
oo i didnt think i could do that
phi
  • phi
next he gave away 1/3 of his marbles. If you give away 1/3 what fraction do you have left ?
phi
  • phi
** 2x is not the same as x^2
anonymous
  • anonymous
subtract
phi
  • phi
if you divide your stuff into 3 piles and give away 1 pile, how many piles do you have left ?
anonymous
  • anonymous
2
phi
  • phi
yes, and each pile is 1/3 of the all your stuff. you will have 2/3 of your stuff (and gave away 1/3) that is what Allen did. He has 2/3 of his marbles. He has 2x marbles so we say he has 2/3 of 2x or in "math" 2/3 * 2x
anonymous
  • anonymous
4x/3?
phi
  • phi
finally we know that he now has 16 marbles at the end of the day we can write \[ \frac{4x}{3} = 16\]
anonymous
  • anonymous
thank you:)
phi
  • phi
now to find x, we multiply by the reciprocal of 4/3 . multply both sides by 3/4
anonymous
  • anonymous
ooo we're not done?
phi
  • phi
almost done. we want to find x (which is the number of marbles he started with) \[ \frac{4x}{3}\cdot \frac{3}{4} = 16 \cdot \frac{3}{4}\]
anonymous
  • anonymous
12
phi
  • phi
on the left side. the 3 in the bottom divides into the 3 up top and you get 1. (they "cancel") same for the 4's we get x= 16/4 *3 or x= 4*3 x=12
anonymous
  • anonymous
:) thanks

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