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Scott C.

Mathematics educator with 16+ years exp.

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Geometry

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Question:

A window 15 meters above the base of the building is reached by the top end of a 25 meter long ladder. How far is the bottom end of the ladder from the base of the building?

Scott C.

Answer:

This problem can be solved using the Pythagorean Theorem ( the square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a & b)). The physical equation looks like this: a^2 + b^2 = c^2 If we let 15 be one of the legs (sides) of the right triangle and 25 be the hypotenuse, the equation becomes this: 15^2 + b^2 = 25^2 Simplifying, 225 + b^2 = 625 (15*15 = 225, 25*25 = 625) Subtracting quantity 225 from both sides, b^2 = 400 (625-225 = 400) Using the square root function, b = 20 (the square root of 400 is 20 (20*20 = 400)) Thus, the bottom end of the ladder is 20m from the base of the building.

Pre-Algebra

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Question:

Simplify the following using the order of operations: 3^2 + 6 *(5 + 4)/3 - 7

Scott C.

Answer:

Order of Operations (PEMDAS) states you must do operations in parentheses first: 3^2 + 6*(9)/3 - 7 {5 + 4 = 9} PEMDAS states you must do operations with exponents next: 9 + 6*(9)/3 - 7 {3 to the 2nd power (3*3) = 9} PEMDAS states you must do operations involving multiplication & division next (from left to right): 9 + 54/3 - 7 {6*9 = 54} 9 + 18 - 7 {54/3 = 18} PEMDAS states you do operations involving addition and subtraction last (from left to right): 27 - 7 {9 + 18 = 27} 10 {27 - 7 = 10} The final answer is 10.

Algebra

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Question:

Bob is currently 3 years older than twice his son, Julian's, age. The sum of Julian's and Bob's ages is 87. What are each of their current ages?

Scott C.

Answer:

First, we must start by writing equations to represent each statement in the problem: B can represent Bob's current age. J can represent Julian's current age. 1. B = 3 + 2J (Bob is currently 3 years older than twice his son, Julian's, age) 2. B + J = 87 (The sum of Julian's and Bob's ages is 87) Substituting "3 + 2J" into the 2nd equation for the value of B yields the following new equation: (3 + 2J) + J = 87 Simplifying, 3 + 3J = 87 Subtracting the quantity 3 from both sides, 3J = 84 Dividing both sides by 3, J = 28 (Therefore, Julian's current age is 28) Substituting Julian's age in to the first equation yields: B = 3 + 2(28) Simplifying, B = 3 + 56 = 59. (Therefore, Bob's current age is 59)

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