# I have sold 2/3 of my pencils for $ 0.15 each . If i have 8 pencils left how much money did i collect for the pencils i sold.

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Let x be the number of total pencils you had before you started selling.

What you are trying to figure out first of all is the value of x. To do that, you can set up the following equation:

8/x = 1/3

This is because if you have sold 2/3 and have 1/3 left, 8 is 1/3 of the original. To find for x, cross-multiply. When you do that you get

x = 24

That means you have sold 16 so as to have 8 left.

Now multiply 16 by .15.

That gets you

$2.40.

This means you had 12 pencils to begin with.

Let the total number of pencils you had for selling be X.

Now you have sold 2/3 of your pencils for 15 cents each. Therefore you have 1/3 of your pencils left or in terms of X you have X/3 pencils left.

Now X/3 = 8

=> X= 24

The number of pencils you sold is 16.

So at the rate of 15 cents per pencil you collected 15 * 16 = 240 cents.

**The money you have collected by selling your pencils is $2.4**

The sold out part of pencils = 2/3.

So if I have x pencils, the number of sold pencils = 2x/3.

The rate of each pencil = $0.15

Therefore the amount of sale of 2x/3 pencils = $(2x/3 *0.15) = $0.1x....(1)

The part of pencils left outs unsold= x-2x/3 = x/3.

But x/3 part of pencils = 8.

Or x/3 = 8

x = 3*8 = 24.

So the number of pencils initially I had = 24.

The number of pencils sold = (2/3)24 = 16.

The amount of sale by 16 pencils = $16*0.15 = $0.24.

We don't know the total number of pencils, therefore we'll put the total number of pencils as x.

If you've sold (2/3)*x, you've had (1/3)*x left.

We know, from enunciation that the amount of left pencils is 8.

We'll put (1/3)*x = 8.

We'll cross multiply and we'll get:

x = 8*3

x = 24 pencils

Now, we'll found the amount of sold pencils, namely 2x/3.

We'll substitute x by 24 and we'll get:

2*24/3 = 2*8 = 16 pencils sold

**To compute the cash earned for sold pencils, we'll multiply 16 by $0.15.**

**16*0.15 = $2.40**