Let's solve the problem step by step.
The question involves determining which age ranges new drivers must fall within to be required to take a driver education course to receive a learner permit. We are given multiple choices, and we need to identify the most plausible pair of ages.
First, we need to convert the fractions in the choices to decimal numbers or understand their approximate values:
1. [tex]\( 1812 \)[/tex]
2. [tex]\( \frac{151}{2} \approx 75.5 \)[/tex]
3. [tex]\( \frac{171}{2} \approx 85.5 \)[/tex]
4. [tex]\( \frac{141}{2} \approx 70.5 \)[/tex]
5. [tex]\( \frac{171}{2} \approx 85.5 \)[/tex]
6. [tex]\( \frac{151}{2} \approx 75.5 \)[/tex]
7. [tex]\( 1812 \)[/tex] and [tex]\( 16 \)[/tex] is straightforward.
Now let's review the provided options:
- Option 1: [tex]\( 1812 ; \frac{151}{2} \)[/tex]
[tex]\( 1812 \)[/tex] is an implausibly high age for a new driver. So this option isn't reasonable.
- Option 2: [tex]\( \frac{171}{2} ; \frac{141}{2} \)[/tex]
This option translates to ages of approximately 85.5 and 70.5, which are also not plausible for learner permits.
- Option 3: [tex]\( \frac{171}{2} ; \frac{151}{2} \)[/tex]
This option translates to ages of approximately 85.5 and 75.5, both of which are too old for new drivers who need a learner permit.
- Option 4: [tex]\( 1812 ; 16 \)[/tex]
Once again, an age of 1812 is not plausible.
Upon reviewing the translations and evaluating the plausibility of each pair of ages, it becomes clear that none of the given ranges directly suggest a realistic scenario for new drivers. However, the options should logically point towards typical learner permit age ranges, thus leaving us to infer which pairages lie within the boundaries closest to a typical learner's permit scenario.
Thus, based on the typical new driver's age range and the choices given, it seems that the correct pairs are:
- Option 3: 17.5 years and 15.5 years
These values fit into the plausible range for new drivers:
New drivers under the age of [tex]\( 17.5 \)[/tex] years and over the age of [tex]\( 15.5 \)[/tex] years must take a driver education course to receive a learner permit.
So the correct answer is:
Option 3: [tex]\( \boxed{3} \)[/tex]
