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August's Problem
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David removes 30% of the water in a jar. He then removes 40% of what remains in the jar. What percent of the original amount of water is now in the jar?

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A solution to this problem will appear along with next month’s problem.
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July's Problem
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If 3/4 of a certain number is 36, what is 2/3 of that same number?

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METHOD 1: Make two diagrams
Use a rectangle to represent the number. In Diagram 1 each box represents ¼ 's of the number. Since ¾ of the rectangle represents 36, each box represents 12 and the complete rectangle represents 48. In Diagram 2, the same rectangle is divided into thirds, so that each box now represents 16. Then 2/3 of the rectangle is 32.

 

METHOD 2: Make one diagram
Use a rectangle to represent the number (Diagram 3). Divide the rectangle vertically into quarters (the yellow & green represent the 3/4) and horizontally into thirds (the blue & green represent the 2/3). The entire rectangle is broken into 12 boxes. The 3 quarters are columns of 12, so each of the small boxes is 4. The 2/3's is two rows of 16 (or 8 small boxes) which equals 32.

METHOD 3: Divide and multiply by fractions
Since ¾ of the number is 36, the number is 36 divided by ¾, which is 48. Then 2/3 of 48 is 32.

 

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June's Problem
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If the length of a rectangle is reduced by 3 meters and the width is increased by 2 meters, the result is a square whose area is the same as that of the rectangle. What is that area?

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METHOD 1: Make a chart
In the table shown at right, after values are assigned to the side-length of the square, the rectangle's corresponding dimensions are computed and then the areas of both figures. The area, 36 sq m, is the number common to the last two columns.
METHOD 2: Use algebra
If x is the side-length of the square, then the dimensions of the rectangle are x + 3 and x - 2.
Their areas, respectively are x^2 and (x + 3)(x - 2). Thus x^2 = (x + 3)(x - 2).
This becomes x^2 = x^2 + x - 6, which simplifies to x - 6 = 0.
So, x = 6 and the area is 36 sq m.
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For many additional problems we highly recommend the following books:

Math Olympiad Contest Problems for Elementary and Middle Schools by Dr. G. Lenchner
and
Math Olympiad Contest Problems Volume 2 edited by Richard Kalman
and
MOEMS® Contest Problems Volume 3
edited by Richard Kalman & Nicholas J. Restivo.
are sources of many such problems.

Creative Problem Solving in School Mathematics 2nd Edition by Dr. George Lenchner
can help you to teach solving these types of problems