Directions: Study the table and answer the question that follows.

The table gives the total number of notebooks sold by five stationery counters on a particular day, along with the ratio of hardcover notebooks to softcover notebooks sold by each counter.

Stationery Counters	Total Notebooks Sold	Hardcover Notebooks : Softcover Notebooks
A	135	5:4
B	140	9:5
C	180	4:5
D	160	13:19
E	150	7:8

Find the difference between the mean number of hardcover notebooks sold by counters B, C, and E and the mean number of softcover notebooks sold by counters A, C, and D.

Correct Answer: The correct answer is 5.

Step-by-step Explanation:

To find the difference between the mean number of hardcover notebooks sold by counters B, C, and E and the mean number of softcover notebooks sold by counters A, C, and D, we first calculate the exact number of hardcover and softcover notebooks sold by each counter using the given total sales and ratios.

Step 1: Calculate the number of hardcover notebooks sold by counters B, C, and E.

Counter B:
Total notebooks sold = 140
Ratio of Hardcover to Softcover = 9 : 5
Total parts = 9 + 5 = 14

Hardcover notebooks sold by B = $\frac{140\times 9}{14}$ = 90

Counter C:
Total notebooks sold = 180
Ratio of Hardcover to Softcover = 4 : 5
Total parts = 4 + 5 = 9

Hardcover notebooks sold by C = $\frac{180\times 4}{9}$ = 80

Counter E:
Total notebooks sold = 150
Ratio of Hardcover to Softcover = 7 : 8
Total parts = 7 + 8 = 15

Hardcover notebooks sold by E = $\frac{150\times 7}{15}$ = 70

Mean number of hardcover notebooks sold by B, C, and E:

Mean_H = $\frac{90+80+70}{3}$ = $\frac{240}{3}$ = 80

Step 2: Calculate the number of softcover notebooks sold by counters A, C, and D.

Counter A:
Total notebooks sold = 135
Ratio of Hardcover to Softcover = 5 : 4
Total parts = 5 + 4 = 9

Softcover notebooks sold by A = $\frac{135\times 4}{9}$ = 60

Counter C:
Total notebooks sold = 180
Ratio of Hardcover to Softcover = 4 : 5
Total parts = 4 + 5 = 9

Softcover notebooks sold by C = $\frac{180\times 5}{9}$ = 100

Counter D:
Total notebooks sold = 160
Ratio of Hardcover to Softcover = 13 : 19
Total parts = 13 + 19 = 32

Softcover notebooks sold by D = $\frac{160\times 19}{32}$ = 95

Mean number of softcover notebooks sold by A, C, and D:

Mean_S = $\frac{60+100+95}{3}$ = $\frac{255}{3}$ = 85

Step 3: Calculate the difference between the two means.

Difference = Mean_S - Mean_H

Difference = 85 - 80 = 5

Therefore, the required difference is 5.