J.C. Nichols department store reports that the average sales on Saturdays is twice that on Thursdays and the average sales on Thursdays is twice that on the other four days.What fraction of the weekly sales are made on Thursdays?
a. 1/7
b. 1/5
c. 2/7
d. 1/3
e. 2/5
please answer and explain
Thu sales = $X
Sat sales = $2X
Other 4 days = $X/2
X/(x+2X+X/2) = X/(3 1/2)x = X/(7x/2) =
x * 2/7x = 2/7.
To answer this question, we need to follow the information given in the statement.
Let's assume that the average sales on a regular weekday (Monday, Tuesday, Wednesday, Friday) is represented by "x".
According to the statement, the average sales on Thursdays are twice that on the other four weekdays. Therefore, the average sales on Thursdays would be 2x.
And it is also given that the average sales on Saturdays are twice that on Thursdays. So, the average sales on Saturdays would be 2 * 2x = 4x.
To find the fraction of the weekly sales made on Thursdays, we need to add up the sales on all the days and then calculate the sales made on Thursdays as a fraction of the total weekly sales.
Total weekly sales = sales on Monday + sales on Tuesday + sales on Wednesday + sales on Thursday + sales on Friday + sales on Saturday
From the information given, sales on Thursday = 2x
Sales on Saturday = 4x
Sales on Monday, Tuesday, Wednesday, and Friday are all equal to x.
Total weekly sales = x + x + x + 2x + x + 4x = 9x
Fraction of the weekly sales made on Thursdays = sales on Thursday / total weekly sales = 2x / 9x = 2/9
Now, we have figured out that the fraction of the weekly sales made on Thursdays is 2/9. However, we need to find the answer in the given options.
Looking at the options:
a. 1/7
b. 1/5
c. 2/7
d. 1/3
e. 2/5
None of the options match 2/9 exactly. However, we can simplify the fraction 2/9 to a fraction with a denominator of 7:
2/9 = (2/9) * (7/7) = 14/63
Comparing this to the options, we see that the closest match is option c. 2/7.
Therefore, the answer and explanation is:
The fraction of the weekly sales made on Thursdays is 2/7 - option c.