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Math Help - Help with story problems!

  1. #1
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    Help with story problems!

    1. Eric is allowed to choose his own telephone number. The first digits are set 425-. He can suggest any combination of numerals for the last four digits. Unfortunately, while in first grade, Eric had a great deal of trouble writing the number 8 and has hated the number ever since. How many possible telephone numbers can he construct avoiding the number 8?


    2. Trevor set out on a trip. He needs to travel a total of 4500 miles. He has just had the tires on his car replaced with some very inexpensive ones from Gray's Bargain Barn that will last exactly 3000. What is the least number of spare tires of the same variety he will need to take along to complete the trip? Explain. (Is this a trick question he'll need 4 more right? ) Thanks!

    3. In Kansas many fields have circular irrigation systems. A single sprinkler is placed in the center of the field. If the sprinkler sprays water just to the four edges of the field, what percent of the field is not watered?


    4. A number that is a palindrome reads the same forward and backward. 90 three-digit plaindormes adn 90 four-digit palindromes exist. How many five-digit palindromes exist?

    Thanks, any help would be much appreciated!
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  2. #2
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    Quote Originally Posted by epetrik View Post
    1. Eric is allowed to choose his own telephone number. The first digits are set 425-. He can suggest any combination of numerals for the last four digits. Unfortunately, while in first grade, Eric had a great deal of trouble writing the number 8 and has hated the number ever since. How many possible telephone numbers can he construct avoiding the number 8?
    For each of the last four digits, there are nine possible digits to choose from (since we cannot use 8). So the number of possible telephone numbers would be
    9 x 9 x 9 x 9 = 6,561.

    4. A number that is a palindrome reads the same forward and backward. 90 three-digit plaindormes adn 90 four-digit palindromes exist. How many five-digit palindromes exist?
    900. There are 9 possible choices for the 1st/5th digit (because you can't use zero), 10 possible choices for the 2nd/4th digit, and 10 possible choices for the 3rd digit. So 9 x 10 x 10 = 900.


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    Last edited by yeongil; July 12th 2009 at 03:35 PM. Reason: Added #4
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  3. #3
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    Quote Originally Posted by epetrik View Post
    3. In Kansas many fields have circular irrigation systems. A single sprinkler is placed in the center of the field. If the sprinkler sprays water just to the four edges of the field, what percent of the field is not watered?
    I'm assuming that the field is a square. It sounds like to me that we are comparing the area of a circle with a square, where the length of the diameter of the circle is the same as the length of the side of a square.

    If you have a circle with radius r, then the length of the side of a square is 2r. You should know the area of a circle formula:
    A = \pi r^2
    and the area of a square formula:
    A = s^2 = (2r)^2 = ????

    To find the percentage of the field that is not watered, subtract the area of the circle from the area of the square. Then take that result and divide by the area of the square. You'll get a decimal, so then convert to percent.


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