sam bought some apples at 60c each and sold all but 5 of them at $1,00 each. if he made a profit of $5,00, how many apples did he originally buy?

Question

Sam bought some apples at 60c each and sold all but 5 of them at $1,00 each. if he made a profit of $5,00, how many apples did he originally buy?

Answer 1

Let x=number of Apples Sam bought

 

Translate:

  "Sam bought some apples at 60c each"   means        spent = $0.60x

  "sold all but 5 of them at $1.00 each"      means     earned = $1(x-5)

 

Math:

      earned        -        spent         =         profit

      $1.00(x-5)       -       $0.60x   =        $5.00

 

       $1.00x - $5.00   -   $0.60x    =      $5.00       [expand]

       ($1.00 - $0.60)x   - $5.00     =     $5.00        [combine terms]

        $0.40x = $10.00             [add $5.00 to both sides]

           x = 25 apples

 

Checking (very important):

   Sam bought 25 apples for $0.60 each ($15.00) and sold all but 5 (that is, 20) at $1.00 each (total $20.00) and made a profit of $5.00 ($20.00 - $15.00 = $5.00)     YES!

 

Answer 2

We have a bit of information that we can track to find out how many apples Sam originally brought. We know that he sold the apples at a price of $1.00, and whatever the amount of apples he brought we know he still has 5 remaining. Thus, we get $1.00(a-5) for the amount of money he made selling the apples at $1.00 a piece. The profit needs to be equal to $5.00. We can attain this by subtracting the how much he paid for each apple from the money he made. The equation looks like the below:

 

$1.00(a-5) -$0.60(a-5) = $5.00

$1.00a - $5.00 - $0.60a - $3.00 = $5.00

 

$0.40a -$7.00 = $5.00

 

$0.40a = $12.00

 

a = 30