Question

AUTO RACING At a race car driving school,
there are safety requirements.
UR FAST
DRIVING SCHOOL
RULES TO QUALIFY
18 years of age or older
Good physical condition
Under 6 ft 7 in. tall
Under 295 lb
a. Define the variables, and write a system of
inequalities to represent the height and weight
requirements in this situation. Then graph the system.
b. Name one possible solution.
c. Is (50, 180) a solution? Explain.

Answer 1

9514 1404 393

Answer:

  a. h < 79; w < 295

  b. (h, w) = (60, 280)

  c. yes

Step-by-step explanation:

a.

We can define h and w to represent the height in inches and the weight in pounds. Then the inequalities representing the given restrictions are ...

  h < 79 . . . . . . . . height is less than 6'7"

  w < 295 . . . . . . weight is less than 295 pounds

The graph is attached. The solution space is the area where the solutions to the inequalities overlap.

__

b.

A 5 ft person weighing 280 pounds would meet the given restrictions.

  (h, w) = (60, 280) . . . . is a possible solution

__

c.

  (50, 180) is a solution. The height of 50 inches is less than 79 inches, and the weight of 180 pounds is less than 295 pounds. (A person with these measurements would be quite obese.)

_____

Additional comments

As a practical matter, healthy 18-year-olds will generally have a height greater than 59 inches and a weight greater than 95 pounds. Less than 3% of the population will be shorter or lighter than that.

"Good physical condition" may require a body mass index within a certain range. This will put additional (rather narrow) limits on height and weight. We have only shown inequalities and a graph for the specific conditions listed in the problem statement.