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SOURCE:COMPETITION Number of Problems: 9. FOR PRINT ::: (Book)
Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members are in the League?
Since T-shirts cost dollars more than a pair of socks, T-shirts cost dollars.
Since each member needs pairs of socks and T-shirts, the total cost for member is dollars.
Since dollars was the cost for the club, and was the cost per member, the number of members in the League is .
You and five friends need to raise dollars in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise?
There are 6 people to split the dollars among, so each person must raise dollars.
As shown below, convex pentagon has sides , , , , and . The pentagon is originally positioned in the plane with vertex at the origin and vertex on the positive -axis. The pentagon is then rolled clockwise to the right along the -axis. Which side will touch the point on the -axis?
The perimeter of the polygon is . Hence as we roll the polygon to the right, every units the side will be the bottom side.
We have . Thus at some point in time we will get the situation when and is the bottom side. Obviously, at this moment .
After that, the polygon rotates around until point hits the axis at .
And finally, the polygon rotates around until point hits the axis at . At this point the side touches the point . So the answer is