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Apr 2021 challenge

Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

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  1. A group of friends decided to divide the $800 cost of a trip equally among themselves. When two of the friends decided not to go on the trip, those remaining still divided the $800 cost equally, but each friend’s share of the cost increased by $20. How many friends were in the group originally?
  1. A dairy farmer uses a storage silo that is in the shape of the upright circular cylinder, shown below. If the volume of the silo is π72 cubic metres, what is the diameter of the base of the cylinder, in metres?

  1. Jeremy deposited x pounds in his investment account on January 1, 2001. The amount of money in the account doubled each year until Jeremy had 480 pounds in his investment account on January 1, 2005. What is the value of x?

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Last month's solutions
  1. The turning of Gear A causes Gears B and C to turn as well. If Gear A is rotated by the motor at a rate of 100 rpm, what is the number of revolutions per minute for Gear C?

Solution: 

Since Gear A has 20 teeth and Gear B has 60 teeth, the gear ratio for Gears A and B is 20:60.  Thus the ratio of the number of revolutions per minute (rpm) for the two gears is 60:20, or 3:1.

Similarly, since Gear B has 60 teeth and Gear C has 10 teeth, the gear ratio for Gears B and C is 60:10, and the ratio of the rpms for the two gears is 10:60.

Therefore, if Gear A turns at 100 rpm, then Gear B turns at 100/3 rpm, and
Gear C turns at (100/3) x 6 = 200 rpm.

 
  1. In the figure below, line AD intersects line BE at C. If angle x° =100, what is the value of angle y°?

Solution:

Since angle ABC (x°) = 100°; then angle BCA = 180° – 100° – 20° = 60°.
Since angle BCA = angle DCE; then angle CDE (y°) = 180° – 40° – 60° = 80°.
  1. Between 1497 and 1500, Amerigo Vespucci embarked on two voyages to the New World. According to Vespucci’s letters, the first voyage lasted 43 days longer than the second voyage, and the two voyages combined lasted a total of 1,003 days. How many days did the second voyage last?

Solution:

Let x represent the number of days the second voyage lasted. The number of days the first voyage lasted is then x + 43.
Since the two voyages combined lasted a total of 1,003 days, then x + (x + 43) = 1,003 gives 2x + 43 = 1,003, 2x = 960 and therefore x = 480 days.

 

 

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