Question 1209350
<pre>
Looks like AI got this one correct.  AI will get better and better, but you
can't trust it with everything yet.  There is still some use for us humans.
So I'll do it the human way.
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<font color="blue" size=4>Rama was getting some items for the new school year.</font>

Let x = the amount at first.

<font color="blue" size=4>First, he bought some textbooks with $8 more than 1/3 of his money.</font> 

Let y = how much he had left after buying textbooks.
{{{y=x - (8 + expr(1/3)x)}}}
{{{y=x - 8 - expr(1/3)x}}}
{{{y=expr(2/3)x-8}}} 

<font color="blue" size=4>Next, he bought his stationery with $12.20 less than 1/2 of his remaining money.</font>

Let z = how much he had left after buying stationery.
{{{z=y-(expr(1/2)y-12.20)}}} 
{{{z=y-expr(1/2)y+12.20}}}
{{{z=expr(1/2)y+12.20}}}

<font color="blue" size=4>Lastly, he bought some school socks with $2.80 more than 1/2 of the money left.</font>

Let w = how much he had left after buying socks.
{{{w=z-(expr(1/2)z+2.80)}}}
{{{w=z-expr(1/2)z-2.80}}}
{{{w=expr(1/2)z-2.80}}}

<font color="blue" size=4>Then, he had $15.40 with him.</font> 
{{{w=15.40}}}

{{{system(y=expr(2/3)x-8,z=expr(1/2)y+12.20,w=expr(1/2)z-2.80,w=15.40)}}} 

<font color="blue" size=4>How much money did he have at first?</font>

Substitute the 4th equation in the 3rd equation

{{{15.40=expr(1/2)z-2.80}}}
{{{18.20=expr(1/2)z}}}
{{{36.40=z}}}

Substitute that in the 2nd equation

{{{36.40=expr(1/2)y+12.20}}}
{{{24.20=expr(1/2)y}}}
{{{48.40=y}}}

Substitute that in the 1st equation

{{{48.40=expr(2/3)x-8}}}
{{{56.40=expr(2/3)x}}}
{{{169.20=2x}}}
{{{84.60=x}}}

Answer: $84.60   <--SOLUTION!

Checking:

He had $84.60 
<font color="blue" size=4>First, he bought some textbooks with $8 more than 1/3 of his money.</font> 

1/3 of his 84.60 or 28.20, plus 8 is 36.20, which was what he spent,
so he had 84.60-36.20 or 48.40 left.

<font color="blue" size=4>Next, he bought his stationery with $12.20 less than 1/2 of his remaining money.</font> 

1/2 of his remaining money was 1/2 of 48.40, or 24.20, minus 12.20, or 12, 
which was what he spent, so he had 48.40-12 or 36.40 left.

<font color="blue" size=4>Lastly, he bought some school socks with $2.80 more than 1/2 of the money left.</font>

1/2 of his remaining money was 1/2 of 36.40, or 18.20, plus 2.80, or 21, 
which was what he spent, so he had 36.40-21 or 15.40 left.

<font color="blue" size=4>Then, he had $15.40 with him.</font>

So now we know we have the right answer, $84.60.

Edwin</pre>