Determine how many licence plates would cost $100

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In summary, the cost for producing a license plate in this state is $n for each digit n > 0 and $10 for each digit 0. For letters, the cost is proportional to the position in the alphabet. To determine how many license plates would cost $100, we can use linear programming and the answer is 1287 license plates.
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WMDhamnekar
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In a certain state of a certain country, each vehicle license plates have exactly three letters followed by three digits. We are told that to produce such a license plate, it costs $n for each digit n>0 and $10 for each digit 0. For letters the cost is proportional to the position of the letter in the alphabet, namely \$1 for A, \$2for B, so on and so forth, upto $26 for Z.

Now, how to determine how many license plates would cost $100?

Answer:- I don't understand how to answer this question. I think linear programming will help here.
 
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This question seems to be difficult and maybe linear programming can help here.
 
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Dhamnekar Winod said:
In a certain state of a certain country, each vehicle license plates have exactly three letters followed by three digits. We are told that to produce such a license plate, it costs $n for each digit n>0 and $10 for each digit 0. For letters the cost is proportional to the position of the letter in the alphabet, namely \$1 for A, \$2for B, so on and so forth, upto $26 for Z.

Now, how to determine how many license plates would cost $100?

Answer:- I don't understand how to answer this question. I think linear programming will help here.
Hello,
After working on finding out the answer to this question, eventually i suceeded. The answer to this question is 1287 license plates would cost \$100.

Justification to the answer:-

The maximum possible cost is \$108 of the license plate having ZZZ 000. Finding the number of license plates having the cost of \$100 is equivalent to finding how many ways 8 indistinguishable balls can be put into 6 distinguishable cells. So $\binom{n+r-1=13}{r=8}=1287 $ license plates.
 

FAQ: Determine how many licence plates would cost $100

1. How do you determine the cost of license plates?

The cost of license plates varies depending on the state and type of vehicle. To determine the cost, you can contact your local Department of Motor Vehicles (DMV) or check their website for specific pricing information.

2. What factors affect the cost of license plates?

The cost of license plates can be affected by several factors, including the type of vehicle, the state in which the plates are being purchased, any additional fees or taxes, and the duration of the registration period.

3. Can you provide a general estimate of how many license plates $100 would cover?

It is difficult to provide a general estimate as the cost of license plates can vary greatly. However, in most states, $100 would cover the cost of standard license plates for one vehicle for a period of one to two years.

4. Are there any discounts or exemptions for certain groups or individuals?

Some states offer discounts or exemptions for certain groups or individuals, such as veterans, senior citizens, or individuals with disabilities. It is best to check with your local DMV for specific information on discounts or exemptions.

5. Can the cost of license plates be waived or reduced in any circumstances?

In some cases, the cost of license plates may be waived or reduced, such as for low-income individuals or in cases of financial hardship. These waivers or reductions are typically granted on a case-by-case basis and may require documentation or proof of eligibility. Contact your local DMV for more information.

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