Stumpers 10

1.  To buy a ticket for a weekly state lottery, a person selects 6 integers from 1 to 36, the order not being important.  There are 1,947,792 such combinations of six digits.  Matthew and nine friends want to win the lottery by buying every possible ticket (all 1,947,792 combinations), and plan to spend 16 hours a day doing it.  Assume that each person buys one ticket every five seconds.  What do you think of this plan?  Can the project be completed within a week?

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2. Before you are able to take a bite of your new chocolate bar, a friend come along and takes 1/4 of the bar.  Then another friend comes along and you give this person 1/3 of what you have left.  Make a diagram that shows the part of the bar left for you to eat.

Later you have another chocolate bar.  This time, after you give away 1/3 of the bar, a friend breaks off 3/4 of the remaining piece.  What part of the original chocolate bar do you have left?  Answer this question by drawing a diagram.

7.  Simplify each of the following:

a.  the sum of 6x + 2 and -8x +5

b.  the result of subtracting 5x - 19 from 8x +12

c.  the product of 7x and 4x - 0.

8.  Solve 2/3(3x + 14) = 7x + 6, by first multiplying both sides of the equation by 3, before applying the distributive property.

3.  This year, there are 1,016 students at the zoo, of whom 63 are from Ruffing.  To the nearest tenth of a percent, what part of the student population at the zoo come from Ruffing?

5.  A group of ten persons were planning to contribute equal amounts of money to buy some pizza.  After the pizza was ordered, one person left.  Each of the other nine persons had to pay 60 cents extra as a result.  How much was the total bill?

4.  Ian takes a board that is 50 inches long and cuts it into two pieces, one of which is 16 inches longer than the other.  How long is each piece?

6.  In baseball statistics, a player's slugging ratio is defined to be (s + 2d +3t +4h)/b, where s is the number of singles, d the number of doubles, t the number of triples and h the number of home runs obtained in b times at bat.  Luke came to bat 75 times during the season, and hit 12 singles, 4 doubles, 2 triples, and 8 home runs.  What is Luke's slugging ration, rounded to three decimal places?

9.  If m and n stand for integers, then 2m and 2n stand for even integers.  Explain.  Use the distributive property to show that the sum of any two even numbers is even.

Show that the sum of any two odd numbers is even.