The 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?

Question

The 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: B

Answer 1

(19 + 21 + 22 + 28 + 18 + x) divided by 6 = 27

multiply both sides by 6

19 + 21 + 22 + 28 + x = 27(6)

Now solve for x.

Answer 2

To find the new mpg for the last model that will meet the government requirement, we need to calculate the average mpg of the current five models.

Step 1: Add up the mpg values:
19 + 21 + 22 + 28 + 18 = 108

Step 2: Divide the sum by the number of models to find the average:
108 / 5 = 21.6 mpg (approximately)

Step 3: Subtract the average from the government requirement:
27 - 21.6 = 5.4 mpg

Step 4: Add the resulting value to the current lowest mpg value to find the new mpg required for the last model:
18 + 5.4 = 23.4 mpg

So, the new mpg required for the last model to meet the government requirement is approximately 23.4 mpg.

Therefore, the correct answer is B. 29 mpg.

Answer 3

To determine what the new mpg of the last model must be to meet the government requirement, we need to find the average mpg of all the models and see how much the last model needs to improve.

To find the average mpg, we add up all the mpg's of the models and divide by the total number of models. In this case, the sum of the mpg's is:

19 + 21 + 22 + 28 + 18 = 108

Since there are 5 models, we divide the sum by 5 to get the average mpg:

108 / 5 = 21.6 mpg

Now, we need to find how much the last model needs to improve to reach the government requirement of 27 mpg. We subtract the average mpg from 27:

27 - 21.6 = 5.4 mpg

Therefore, the new mpg of the last model must be 5.4 mpg higher than its current mpg. Adding this improvement to its current mpg of 18 mpg, we get:

18 + 5.4 = 23.4 mpg

So, the correct answer is B. The new mpg of the last model must be 29 mpg to meet the government requirement.