Problem of the Week :

Determine three numbers that fit the following pattern :

2 ,8, 4, 10, 5 , 11, 5.5, ___, ___, ___

If the mean of twenty different positive integers is 20, what would be the greatest possible value of any one of these twenty numbers ?

Solution:

210. Use the smallest possible nineteen numbers to determine the largest possible twentieth number. In other words, (1+2+3+4+5+6+7+8+9+11+12+13+14+15+16+17+18+19+x)/20 =20;

190 + x = 400 ; x = 210

One- sixth of a stell beam of a bridge is in cement below the bed of a river. two-fifths of the beam if in the water, and 78 feet of the beam are above the water. How long is the steel beam ?

Solution:

180 feet. Set up the an algebraic equation where x is the length of the steel beam:

(1/6)x + (2/5)x + 78 = x

Multiply both sides of the equation by the common denominator 30.

5x + 12x + 2340 = 30x

17x + 2340 = 13x

x = 180

While John is driving his car, he notices that the odometer reads 13931 miles. The mileage is a palindrome, a number that reaads the same forward as it does backward. Exactly 2 hours later John notices that the odometer displays a different palindrome. What is the most likely average speed at which the car has been traveling ?

Solution:

55 mph. The next palindrome that the odometer can display is 14041. To reach this value, John will have to travel 110 miles. If it takes him two hours , then his average speedis 55mph. The next palindrome , 14141, would mean that the car traveled 210 miles at 105 mph, which is probably unrealistic.

A man was born on February 29,1928. He died on January 29, 2004. How many actual birthdays did he get to celebrate during his life(not including the day he was born as a birhtday) ? Hint: Don't forget about leap years.

Solution:

18 birthdays. Feb. 29 occurs every four years. 2004 is a leap year. He celebrated his Feb. 29 evey four years from 1928 till 2000, but not 2004 . He died before his birthday.

A basket of fruit contains only bananas, apples , and oranges. The basket contains 2 bananas, 6 red apples , and 8 green aplles. If the toal number of pieces of fruit is three times the number of apples in the basket, how many oranges in the basket?

Solution:

26 oranges. There are 6+8 = 14 apples in the bag. There are 3 x 14 = 42 pieces of fruit in the bag. That means the number of oranges would be

42 - 14 - 2 = 26 .

A palindrome is a number that is written in the same forward and backward. Some examples are 11,242 and 909. How many whole-number palindromes exist between 10 and 1000?

Solution:

99 whole-number palindromes

Suppose that you have two different colors of socks in your sock drawer. Assume that none of the socks are bound together. If you pull three socks out of the drawer with out looking at the color, what is the probability that you would have a matched pair of socks?

Solution:

100 percent or 1. Suppose that the socks are red and blue. Let the first sock be blue and the second sock be red. The third sock must be either red or blue, thus a pair is guaranteed.

Solve the problem of the week and get extra credit points. You have to show how you got your work. Submit it on loose- leaf paper with your name and class.Answer will be shown next week.

Using each of the digits 1,2,3,4,5,6, and 8 once, fiil in the balnks to make a true statement:

_____ + _____ x ______divide _____ = _______ x ______ - ________

Solution

Two possible solutions are

2 + 8 x 6 divide 4 = 5 x 3 - 1 and

3 + 8 x5 divide 2 = 6 x 4 -1

The mean of a set of five numbers is known to be 9.4. If four of the numbers in the set ar 7, 11, 15, and 19, what is the missing number?

Solution

Letting x be the missing number, we know the following:

7 + 11 + 15 + 19 + x / 5 = 9.4

52 + x / 5 = 9.4

52 + x = ( 9.4 ) (5)

52 + x = 47

x = 47 - 52

x = - 5 so the missing number is -5.

A girl who is four and a half feet tall is standing next to a telephone pole. A t 1:00 p.m. , the girl casts a shadow 8 feet long, and the telephone pole casts a shadow 36 feet long. How tall is the telephone pole?

Solution: 243 inches , or 20 feet 3 inches. You can set up a proportion. Convert measurement to inches. the girl's height is 54 inches, and her shadow 's length is 96 inches. The pole's height is unknown and the shadow of the pole is 432 inches long.

girl's height/ lenght of gir's shadow = pole's height/ length of pole's shadow

54 / 96 = x / 432

(54) (432) = 96x

23,328 = 96x

243 = x therefore, the height of the poleos 243 inches, or 20 ft. 3 inches.