Grant T.

3/16/03

 

Let y = price to develop pictures.

Let x = number of pictures being developed.

The equation is,

3+.04x = y                                                

y = 2+.07x

 

To Solve this equation you must go through the following steps:

 

1.  3+.04x = 2+.07x                                                  To check the answer:

    -2 -.04x   -2 -.04x                                                                _         _

                                                                                  3+.04(33.3) = 4.3

2.  1 = .03x                                                                3+1.3  _      = 4.3

    .03  .03                                                                  4.3 = 4.3

                _

3.  x = 33.3                                                                   An Explanation

                                                                                  How I came up with the

To Solve for y:                                                                   equations

                    _                                                            A store called Fast Photos

1.  3+.04(33.3) = y                                                    charges 2$ + an additional

     3+1.3          = y                                                     .07$ for each photo you want

        _                                                                        to develop. This gives us

2.  4.3 = y                                                                  y = 2+.07x.  Let y = total

                                                                                                price to develop pictures.                            

Let x = number of pictures being developed.  A store competing with Fast Photos, called Quick Photos, charges 3$ + an additional .04$ per photo.  Through this info., I came up with the equation y = 3+.04x.

How to start solving the equation

To solve this equation, I first decided to substitute the Fast Photos equation into the Quick Photos equation.  Because in the Fast Photos equation, y = 2+.07x, when I rewrote the Quick Photos equation, I replaced y with 2+.07x.  We can see this in the equation

3+.04x = 2+.07x.  Once we had this base equation, we had to try to isolate the x’s.  I did this by subtracting both 2 and .04x from both sides of the equation.  This left me with the equation 1 = .03x. To isolate the x, I divided both sides by .03, leaving me with x = 33.3.  Now that we know what x equals, it is time to solve for y.

Solving For y

To solve for x, I looked at my base equation (y = 3+.04x) and replaced all_instances of x with 33.3repeating.  I found myself stuck with the equation y = 3+.04(33.3).  Following the order of operations, I first multiplied .04 with 33.3.  This left me with

y = 3+1.3repeating.  Y = 4.3.

The Answer & What the x & y Variables Tell You

The answer is that x = 33.3repeating and y = 4.3repeating.  But what does this all mean?  Because the x variable tells you how many photos are being developed, 33.3 is the number of photos you have to develop in order for Quick Photos to be just as good a deal as Fast Photos.  So how many $ would it cost to develop 33.3 photos.  The y variable gives you this information.  No matter where you go to develop your photos, if you plan on developing 33 photos, it will cost you 4 dollars and 33cents.