: Algebra I Variables in Algebra
: Goal 1: Evaluating Variable Expressions A variable is a letter that is used to represent one or more numbers. The numbers are the values of the variable. A variable expression is a collection of variables, numbers, and operations. Here are some examples: 8y 16/b 4 + s 9 - x The expression 8y is usually not written as 8 x y because of possible confusion with the variable x. Replacing each variable in an expression by a number is called evaluating the expression. The resulting number is the value of the expression.
: Title Steps to Success 1. Write the variable expression.2. Substitute values for variables. 3. Simplify the numerical expression.
: Evaluating a Variable Expression Evaluate the expression when y = 2. a. 8y = 8(2) Substitute 2 for y. 16 Simplify. b. 10/y = 10/2 Substitute 2 for y. 5 Simplify.
: Evaluating a Real-Life Expression Average speed is given by the following formula. Average Speed = Distance/Time = D/T Find the average speed (in miles per hour) of a car that traveled 180 miles from Boise, Idaho, to the Minidoka National Wildlife Refuge in 3 hours. Average Speed = D/T Write expression = 180/3 Substitute values for variables = 60 Simplify. The average speed was 60 mph.
: Evaluating a Geometric Expression The perimeter of a triangle is equal to the sum of the lengths of its sides: a + b + c. Find the perimeter of a triangle that's sides are 8, 17, and 15. The dimensions are in feet. Perimeter = a + b + c Write expression = 8 + 15 + 17 Substitute values for variables. = 40 Simplify. The perimeter of the triangle is 40 feet.
: Evaluating Simple Interest The simple interest earned by money P (called the principal) at an annual interest rate r for t years is given by Prt. You deposit $650 at a rate of 8% per year. How much simple interest will you earn after one half of a year? Simple Interest = Prt Write expression = (650)(0.08)(0.5) Substitute values for variables = 26 Simplify After one half of a year, you will have $26 of simple interest.
: Goal 2: Modeling a Real-Life Situation Writing the units of each variable in a real-life problem helps you determine the units for the answer. This is called unit analysis and it is often used in problem solving in science. When the same units of measure occur in the numerator and the denominator of an expression, you can cancel the units. In real-life problems, you may need to translate words into mathematics. One way to do this is to use a verbal model.
: Finding Time You plan to go hiking in the Jedediah Smith Redwoods State Park in California. You estimate you'll hike at a rate of 2 miles per hour on a steep trail. How long will it take you to hike from Howland Hill Road along the Boy Scout Tree Trail and back? Let's say that the distance for the round-trip is 7.4 miles.
: Problem-Solving Strategy Verbal Model- Time = Distance/RateLabels- Time = t (hours) Distance = 7.4 (miles) Rate = 2 (mph)Algebraic Model- t = 7.4/2 = 3.7It should take you about 3.7 hours to hike the Boy Scout Tree Trail.
: Using Unit Analysis Use unit analysis to check that hours are the units of the solution. Time = Distance/Rate = mi/mi-h = mi ( h/mi) = h
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