Question 985982
Jasmine and her friends eat half a bag of lollies on her birthday.  The next day
they eat three quarters of the number they ate the day before.  Then there are 8
lollies left.  How many were in the bag to begin with?
<pre>
There are two ways to do it, with and without algebra. I'll do it both ways:

FIRST WAY (WITHOUT ALGEBRA):

Start at the end and go backwards.

There were 8 lollies left. 

Therefore since 8 were left after taking three quarters, the 8 must have been
the one quarter that was left, so there were 4 times 8 or 32 lollies before.

Then before that they ate half a bag, so those 32 must have been half of what
they started with, so they started with 64 lollies.

SECOND WAY (WITH ALGEBRA)

There were N lollies to begin with 
</pre>
Jasmine and her friends eat half a bag of lollies on her birthday.  
<pre>
So there was half a bag or {{{expr(1/2)N}}} left
</pre>
The next day they eat three quarters of the number they ate the day before. 
<pre>
Since they ate {{{expr(1/2)N}}} the day before, they ate {{{expr(3/4)*expr(1/2)N}}}, so we subtract that from what they had left.
So after that, the had this many left:

{{{expr(1/2)N}}}{{{""-""}}}{{{expr(3/4)*expr(1/2)N}}}  

Multiplying those two fractions

{{{expr(1/2)N-expr(3/8)N}}} 
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Then there are 8 lollies left.  
<pre>
So we set that equal to 8

{{{expr(1/2)N-expr(3/8)N}}}{{{""=""}}}{{{8}}}

Multiply through by LCD = 8

{{{4N-3N=64}}}

{{{N=64}}}

Same answer as when we didn't use algebra and worked backwards.

Edwin</pre>