Answer:
"Tanya bought 3 items that each cost the same amt"
"Let x represent the cost of one of Tanya's items"
   So, Tanya bought 3 items, costing x+x+x = 3x
   Note that (number of items)*(cost per item) = (number of items)*(cost/item) = cost,   [item cancels out]
  
"Tony bought 4 items that each cost the same amt, but each was $2.25 less than the items Tanya bought."
  The cost for Tony's items was:  (x-2.25)+(x-2.25)+(x-2.25)+(x-2.25) = 4*(x-2.25)
  
"Tanya and Tony paid the same amt. of money"
    This is an equation (the same amount means equals)
     Tanya's cost = Tony's cost
a.) Write an equation. Let x represent the cost of one of Tanya's items
           3x      =     4(x-2.25)
  
Now, the math:
b.) Solve the equation. Show your work.
           3x      =     4(x-2.25)
           3x  =  4x - 9.00                 [distributive principle; multiply]
          -x = -9.00                      [subtract 4x from both sides; option, could instead add 9.00, then subtract 3x from both sides, getting 9.00=x]
           x = 9.00           [multiply both sides by (-1)]
                  [note:  to "solve for x" means to find the value(s) of x that make the equation true,
                           so let's see if it is true --]
c.) Check your solution. Show your work.
   Is              3x      =     4(x-2.25), when x=9.00    ?
           3(9.00) = 4(9.00-2.25)    ?
            27.00 = 36.00 - 9.00    ?
              27.00 = 27.00    ?yes
  
d) State the solution in a complete sentence.
      The problem started with:  "Tanya bought 3 items that each cost the same amt. Tony bought 4 items that each cost the same amt, but each was $2.25 less than the items Tanya bought. Both Tanya and Tony paid the same amt. of money."
      I would write:   "Tanya bought 3 items, each costing $9.00.  Tony bought 4 items, each costing $6.75.  Tanya and Tony each paid $27.00."   
Step-by-step explanation: