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A bookshop was selling textbooks and workbooks. A textbook cost 3/5 more than a workbook. 35% of the books sold were textbooks. If the price of a workbook was $6, and $108 more was collected from the sales of workbooks than textbooks, how many books were sold altogether?

 Feb 16, 2022
 #1
avatar+122390 
+2

Let the number of textbooks = T

And let the number of workbooks = W

 

If the price of a workbook  was $6, then the price of a textbook  = $6 ( 1 + 3/5)  = $6 ( 8/5)  = $9.60

 

35% of the books sold were textbooks so 65% were workbooks

 

Let the total number of books sold =  S

 

So.....the textbooks = .35S    and the  workbooks  =  .65S

 

Putting all of this together......

 

Number of workbooks sold * cost each - Number of textbooks sold * cost each  =  $108

 

          .65S(6)   -  .35S ( 9.6) =  108         simplify

 

           3.90S -  3.36S  = 108

 

               .54S  = 108

 

                  108 / .54 =  S =   200  books total

 

cool cool cool

 Feb 16, 2022
 #2
avatar+169 
+2

Price of Workbook = $6

Price of Textbook = (3/5)(6) + 6 = $9.6

 

Let T = number of Textbooks

     W = number of Workbooks

      S = total number of textbooks and workbooks

               S = T + W --> equation (1)
    * 0.35S = T --> equation (2)

    * 6W = 108 + 9.6T --> equation (3)

 

 equation (2) in equation (1)

      S = T + W

        S = 0.35S + W

         0.65S = W --> equation (4)

Total sales:

        6W + 9.6T = (108 + 9.6T) + 9.6T

         6W = 108 + 9.6T

                    * T = 0.35 (equation (2))

          6W = 108 + 9.6 (0.35S)

          6W/6 = (108 + 3.36S)/6

            W = 18 + 0.56S --> equation (5)

   equation (4) = equation (5)

      0.65S = 18 + 0.56S

      0.65S - 0.56 S = 18

             0.09S/0.09 = 18/0.09

                  S = 200 books

                200 books was sold altogether

 Feb 20, 2022

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