he federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg’s for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 27 mpg. The last of the models is to be redesigned to meet the government requirement. What must the new mpg of this model be to meet the requirement?
A. 27 mpg
B. 29 mpg
C. 30 mpg
D. 54 mpg
Answer D
To find the new MPG needed to meet the government requirement, we need to calculate the average of the current MPG values and the new MPG for the redesigned model.
1. Start by adding up the current MPG values:
19 + 21 + 22 + 28 + 18 = 108
2. Next, add 27 (the government requirement) to get the total MPG needed for all the models:
108 + 27 = 135
3. Since there are already 5 models, we divide the total MPG needed by 5 to get the average MPG:
135 / 5 = 27
4. Finally, subtract the sum of the current MPG values from the total MPG needed:
135 - 108 = 27
The answer is not D. Instead, the new MPG needed for the redesigned model to meet the government requirement is 27 mpg (Option A).
To find out the required mpg for the last model to meet the government requirement, we need to calculate the average mpg of all the models and use it as a reference.
Step 1: Add up the mpgs of all the models.
19 + 21 + 22 + 28 + 18 = 108
Step 2: Divide the total mpg by the number of models.
108 / 5 = 21.6
Step 3: Subtract the average mpg from the government requirement.
27 - 21.6 = 5.4
Step 4: Add the result from Step 3 to the current mpg of the last model.
18 + 5.4 = 23.4
The new mpg for the last model must be 23.4 mpg to meet the government requirement.
Therefore, the correct answer is not provided.