Effective Algebraic Problem-Solving Strategies
Unleash your algebraic prowess with practical problem-solving techniques involving calculations, equations, variables, translating word problems, and more in this informative module for accounting managers.
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Presentation Transcript
Accounting For Managers Module 2: Calculations and Solving Equations
Variables A variable is a letter that represents a number or quantity whose value may change (ex/ x, y, z, a, t etc) A constant is a number whose value always stays the same To write algebraically, we need some symbols as well as numbers and variables
Solving Single-Step Equations ? + 3 = 8 ? + 3 3 = 8 3 ? = ?
Solving Multi-Step Equations Distributive property: if a, b, c, are real numbers then ? ? + ? = ?? + ?? Simplify: 3 ? + 4 3 ? + 3 4 = ?? + ??
Translating Words Into Algebra Write Algebraic Expressions from Statements: Form ax+b and a(x+b) This video explains how to write algebraic expressions from statements. http://mathispower4u.com Examples: 15 less than x is equal to 26 x - 15 = 26 18 + d The sum of 18 and d 21 > 17 21 is greater than 17 9 times the sum of t and 4 gives 24 9(t + 4) = 24 Twice the difference of x and 3 gives 18 2(x - 3) = 18
Algebraic Problem Solving Strategies Problem solving strategy: 1. Read the word problem 2. Identify what you are looking for 3. Name what you are looking for. Choose a variable to represent that quantity 4. Translate into an equation 5. Solve the equation using good algebra techniques 6. Check the answer in the problem. Does it make sense? 7. Answer the question with a complete sentence
Mark-Up Problems Example 2: Determine a Percent of Change (increase) This video determine a percent of increase from 3200 to 3400. Complete Video Library: http://www.mathispower4u.com amount of mark-up = mark-up rate * wholesale price List price = wholesale price + mark-up
Discount Problems Example: Jason bought a pair of sunglasses from a rack that was labeled $10 off all Retrop brand glasses. The original price of the sunglasses was $39. What was the sales price of the sunglasses? Amount of discount = discount rate(original price) Sale price = original price - discount s = sales price s = $39 - $10 s = $29
Simple and Compound Interest Simple interest equation: Compound interest equation: I = (p)(r)(t) A(t) = P(1 + r)t I = interest paid A(t) = account value p = principal- original amount of t = measured in years money borrowed account; r = interest rate, a per year rate, present value written as a decimal r = annual percentage rate (APR), t = time of the loan, expressed in expressed as a decimal years or portions of a year P = starting amount of
Solving Formulas for a Specific Variable Example: Solve the formula d = rt for t: 1. When d = 520 and r = 65 2. Algebraically When d = 520 and r = 65: Algebraically: d = rt d = rt 520 = 65t 520/65 = 65t/65 t = 8 d/r = rt/r t = d/r
Graphing Points on a Coordinate Plane Aspects of a graph: Ordered pair: An ordered pair, (x, y) gives the coordinates of a point in a rectangular coordinate system. Points on the axes: points with a y-coordinate equal to 0 are on the x-axis, and have coordinates (a,0). Points with an x-coordinate equal to 0 are on the y-axis, and have coordinates (0,b) The origin: the point (0,0) is called the origin. It is the point where the x-axis and y-axis intersect.
Identifying Trends of a Graph What is the overall trend of this graph?
Rate of Change What is the slope of the line on the geoboard? Solution: Use the definition of slope: m = rise/run m = The slope is
Analyzing Graphical Data If you are a retail professional and are given accounting information or other data on a graph, you ll also need to be able to make decisions based on what you can observe and infer.
Quick Review Algebra Variables Solving single and multistep equations Problem solving strategies Why is it important to know how to solve markup, discount, and simple and compound interest problems as a retail professional? Graph analysis: are you able to analyze trends on a graph in order to make decisions as a manager that will better your business?
