# Tutor profile: Scott C.

## Questions

### Subject: Geometry

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?

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.

### Subject: Pre-Algebra

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

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.

### Subject: Algebra

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?

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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