An automotive repair company has four stores in a large city. The owner purchased 7 diagnostic
Computers for the business. The number of cars serviced per store each month is given below along
With the standard quota. If the standard divisor is 79.7, (a)use Webster's method to determine how
Many computers each store should get based on number of cars serviced and (b)write the modified
Divisor used (answers may vary). Round the divisor to the nearest tenth, if necessary.

Question

Quizplus · Accepted Answer

Using Webster's method, we first calculate the car index for each store by dividing the number of cars serviced by the standard divisor of 79.7.

Car index for Store 1 = 2700/79.7 = 33.90 
Car index for Store 2 = 2200/79.7 = 27.63 
Car index for Store 3 = 3200/79.7 = 40.20 
Car index for Store 4 = 1800/79.7 = 22.62

Next, we add up the car indices to get a total of 124.35. We then divide the total car index by the number of computers (7) to get the quota per computer:

Quota per computer = 124.35/7 = 17.76

Finally, we allocate the number of computers based on the number of times the quota fits into each store’s car index.

Store 1: 33.9/17.76 = 1.91 = 2 computers 
Store 2: 27.63/17.76 = 1.56 = 2 computers 
Store 3: 40.2/17.76 = 2.26 = 2 computers 
Store 4: 22.62/17.76 = 1.27 = 1 computer

The modified divisor used will depend on the specific number of computers allocated to each store, so there is no one correct answer for part B. To find the number of computers that each store should get, we will use Webster's method which is given by:

Number of computers for a store = (Number of cars serviced by that store / Total number of cars serviced by all stores) × Total number of computers

Using the standard divisor of 79.7, and the given numbers of cars serviced and quotas for each store, we get the following calculations:

Store 1: (320 / 1400) × 7 = 1.6 computers
Store 2: (400 / 1400) × 7 = 2.0 computers
Store 3: (300 / 1400) × 7 = 1.5 computers
Store 4: (380 / 1400) × 7 = 1.9 computers

However, Webster's method may not distribute the computers fairly if the standard divisor is not an accurate representation of the true relationship between cars serviced and computer need. Therefore, we need to use a modified divisor to ensure a fair distribution.

To find the modified divisor, we sum the number of cars serviced by all stores and divide it by the total number of computers available:

Total number of cars serviced = 320 + 400 + 300 + 380 = 1400
Total number of computers = 7

Modified divisor = 1400 / 7 = 200

We will now use the modified divisor to calculate the number of computers for each store:

Store 1: (320 / 200) × 7 = 11.2 ÷ 7 = 1.6 computers
Store 2: (400 / 200) × 7 = 14 ÷ 5 = 2.8 ÷ 2 = 1.4 computers
Store 3: (300 / 200) × 7 = 10.5 ÷ 7 = 1.5 computers
Store 4: (380 / 200) × 7 = 13.3 ÷ 7 = 1.9 computers

Since we cannot allocate a fraction of a computer, we will round the numbers to the nearest whole number to get the final answer:

Store 1: 2 computers
Store 2: 1 computer
Store 3: 2 computers
Store 4: 2 computers

Therefore, the answer is A, as Store 1 gets 2 computers, Store 2 gets 1 computer, Store 3 gets 2 computers, and Store 4 gets 2 computers.

An Automotive Repair Company Has Four Stores in a Large