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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.

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

 

 

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Last month's solutions

1. A summer camp counsellor wants to find a length, x, in feet, across the lake as represented in the sketch below. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and angles AEB and CDB have the same measure. What is the value of x?

Solution:

Since the angles AEB and BDC have the same measure as well as angles ABE and CBD, triangles (two pairs of congruent corresponding angles). Since the triangles EAB DCB are similar, their corresponding sides are in the same proportion; thus CD/x = BD/EB. Substituting the given values, then CD/x = BD/EB becomes 800/x = 700/1400.

Therefore, x = (800 * 1400) / 700 = 1600 feet.

2. A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck’s revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?

Solution:

Let x = total number of salads sold and y = total number of drinks sold.

x + y = 209, y = 209 – x, and
6.50x + 2.00y = 836.50, 6.5x + 2(209 – x) = 836.5,  4.5x + 418 = 836.5 then, 
4.5 x = 418.5 and
x = 93 salads.

3. How many litres of a 25% saline solution must be added to 3 litres of a 10% saline solution to obtain a 15% saline solution?

Solution:

Let x = the amount, in litres, of a 25% saline solution to be added. 

Then 3(0.10) + 0.25x = 0.15(x + 3), then 0.25x – 0.15x = 0.45 – 0.30 
Therefore, 0.10x = 0.15 or
x = 1.5 litres.

 

 

 

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