Question

@phi

Answer 1

you need to use algebra. If Allen starts with x (x for unknown) marbles
and doubles them, how do you write that ?

Answer 2

x^2?

Answer 3

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 ?

Answer 4

ugh idk

Answer 5

you could say: If I have x and add another x I will double how much I have
x+x is one way

Answer 6

o yea

Answer 7

you can also write x+x as "I have 1 x plus another x, how many x's do I have?"
2x

Answer 8

oo i didnt think i could do that

Answer 9

next he gave away 1/3 of his marbles.

If you give away 1/3 what fraction do you have left ?

Answer 10

** 2x is not the same as x^2

Answer 11

subtract

Answer 12

if you divide your stuff into 3 piles and give away 1 pile, how many piles do you have left ?

Answer 13

2

Answer 14

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

Answer 15

4x/3?

Answer 16

finally we know that he now has 16 marbles at the end of the day
we can write
\[ \frac{4x}{3} = 16\]

Answer 17

thank you:)

Answer 18

now to find x, we multiply by the reciprocal of 4/3 . multply both sides by 3/4

Answer 19

ooo we're not done?

Answer 20

almost done. we want to find x (which is the number of marbles he started with)

\[ \frac{4x}{3}\cdot \frac{3}{4} = 16 \cdot \frac{3}{4}\]

Answer 21

12

Answer 22

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

Answer 23

:) thanks