Word problem

Question

After deducting his commission of 5% of the sale price, an agent returned more than $2413 to the deal. Find the least possible commission

 

How do I solve, more specifically, what do I solve

Answer 1

"Find the least possible commission" means the dollar amount of the sales commission.

 

How to solve:

 

Let x = the sale price (but remember that the problem asks for "least possible commission")

 

Translate:

 " commission of 5% of the sale price, an agent returned more than $2413 "    means

  x  - (5/100)x > $2413

    [note that 5% may be written as (5/100) or 0.05 as needed by the problem]

 

The math (first, solve for x):

    x - (5/100) > 2413

   100x - 5x > 241300     [multiply by +100 retains sense of inequality]

    95x > 241300         [collect terms]

     x > 2413.00     [divide by 100 retains the sense of inequality]

 

The commission is 5% of the sales price, so:

    y = (5/100)x             [let y = commission]

    x = 20y

   substitute:

     20y > 2413

     y > 120.65

 

Now, since the answer must be given in dollars and cents, the commission must be at least (greater than or equal to)  $120.66.

 

Check:

 Is a commission of $120.66 enough to return more than $2413 to the deal?

    y = $120.66

    x = 20y = $2413.20

 But, $120.65 is not:

    x = (20)120.65

    x = $2413     (check!  "more than" is not satisfied)