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SOLVE
Find three consecutive odd integers whose sum is 105."Consecutive" means one after the other.

First copy this problem down in your notebook and then click on "hint", for a step-by-step analysis of the solution.

HINT:

Algebra is one of my favorite subjects
When x=5, evaluate 3x + 6.

HINT: Evaluate the x-term first.

APPLY: 3(5) + 6 = 15 + 6 = 21.

GEOMETRY PROBLEM
T,V,S is an equilateral triangle (see below). The point V is such that the line segment from T to V is perpendicular to the line segment from R to S. CLASSIFY the inner triangle T,V,S by the measures of its angles and its sides.HINT:

Since the line segment from T to S is opposite the right angle, it is the hypotenuse of the right triangle, T,V,S. Also, the angle between sides VS and ST is 60 degrees, because the triangle is equilateral.

APPLY: Set the sum of the measures of the angles of the triangle T,V,S to 180.

Then angle TSV + angle TVS + angle STV = 180.

Substituting "60" for angle TSV and "90" for angle TVS, we get

60 + 90 + angle STV = 180

150 + angle STV = 180

Therefore, angle STV=30.

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We took it when she wasn't looking.

Illustration for the geometry problem (above)

Unique Mathematical Proof
A Dogon myth suggest that Venus and the Moon might have originated together. Click here to see a unique, mathematical proof on this topic.

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