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?

Guest Feb 16, 2022

#1**+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

CPhill Feb 16, 2022

#2**+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 + ~~9.6~~T = (108 + 9.6T) + ~~9.6~~T

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

Slimesewer Feb 20, 2022