When bakery opened this morning , the ratio of the number of pineapple muffins to the number of mango muffinswas3: 2.after 144 pineapple muffins were sold, the ratio of the number of pineapple muffins to the number of mango muffins changed to 3: 5.how many pineapple muffins were there when the bakery opened this morning

             x
Then at opening time.  After 144 pineapple muffins were sold, the
           2x/3    ratio became 

                                            x-144       3
                                            =
                                              2x/3       5.

Let's solve this for x:   5(x-144) = 2x, or 5x - 720 = 2x.  Thus, 3x = 720, and 
x = 240.

There were 240 pineapple muffins in the beginning, and (2/3)(240) mango muffins (160).

After 144 pineapple muffings were sold, 240-144 represents the new count of the pineapple muffings.  The new ratio of pineapple to mango is then

96         3
=             This tells us that our answer (240 pineapple muffins) is 
160        5              correct.