Finding missing amount

Question

Alex spent 25% of his money on a sports drink.  then he spent 25% of the remaining money on trial mix.  He had $9 left.  how much money did Alex have to begin with?

Answer 1

If possible, assign a variable to the amount the problem asks you to find.  Here,
   Let x = amount Alex began with
 
Now, 25% can also be written as 0.25 or ( 25/100 or 1/4 ) as needed.  Let's use (1/4).
 
Translate:
  "Alex spent 25% of his money on a sports drink"    means  Alex now has left  ( x - x/4 )
  "spent 25% of the remaining money on trial mix"   means

           Alex now has left  (x - x/4) - (x - x/4)/4
  "He had $9 left."      means    (x - x/4) - (x - x/4)/4  =  9
 
Now, the easy math:
    (x - x/4) - (x - x/4)/4  =  9
    4(x - x/4) - (x - x/4) = 36        (multiply everything by 4)
     4x - x - x + x/4 = 36               (multiply everything by 4 again)
     16x - 4x -4x + x = 144           (collect terms)
     9x = 144                               (divide both sides by 9)
       x = 16       Alex started with $16.00
 
Checking (very important):
  Alex started with $16 and spent (1/4), so he spent $4.00 and has $12.00 remaining.  Then he spent (1/4) of $12.00 and he now has $9.00 remaining.

Answer 2

Let x represent the amount of money Alex had to begin with.  Then,

 

x-.25x-.25(x-.25x)=9

 

x-.25x-.25x+.0625x=9

 

.5625x=9

 

x=16

 

So, Alex had $16 to begin with.

Answer 3

Let x = the amount Alex had to begin with

 

 

He spent 25% of his money originally.   So we have 0.25x.

 

Then he spends 25% of the remaining amount.  This is 0.25(0.25x).  Spent means that he loses the amount.

 

 

Here is the equation that we get.

 

0.25x - 0.25(0.25x) = 9

 

 

We can solve for x from this equation.

 

0.25x - 0.06x = 9

 

0.19x = 9

 

 

Divide both sides of the equation by 0.19

 

x = 47.37

 

 

He had $47.37 to begin with.