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Overhead Sheets A. 1C Writing equations & inequalities 1 When we write equations or inequalities, we take the written description of a situation, and we represent that situation using mathematical symbols. Example: A boat is 40 times larger than its scale model. Write an equation to represent this relationship. Step 1: Identify your variables b = the size of the boat s = the size of the scale model Step 2: Write the equation “boat is” can be represented by b= b = 40s 2 Practice writing equations for the following situations: (a) Pencils cost $.35 each. Write an equation to calculate the total cost of any number of pencils. (b) A motel charges $50 per night for a room. Write an equation to represent the charge for a stay at the hotel. (c) Bananas cost $.39 per pound. Write an equation to calculate the cost of buying bananas. 3 In some math problems, we have one value which is a constant. That value does not change and does not depend on any other variable. We have other values which are dependent upon some other unit in the problem. Example: You hire an electrician to install a light in your kitchen. The electrician charges $68 for the house call, plus $50 an hour for service. Write an equation to represent the cost of hiring this electrician. c = cost h = # of hours Write the equation Name the constant 4 Practice: (a) To rent a hotel room for one night, a company charges $85 plus $10 per person. Write an equation to calculate the total cost of staying at this hotel. (b) The admission to a state park is $5.00 per vehicle plus $.50 per passenger. Write an equation to represent the total admission to the state park for your family. 5 Function Rule An equation represents a functional relationship. Sometimes we are asked to write a function rule instead of an equation. A function rule is a special type of equation that uses f(x) to represent y. In other words, instead of writing y = you would write f(x) = f(x) means “the value of the function at x” Your independent variable would go inside the parenthesis. Sometimes that variable is “x”, sometimes is it some other letter. 6 Each month Jean’s phone bill includes a $25 basic fee plus a charge of $.07 per minute for the number of minutes of longdistance calls she makes. Write a function rule to describe the total amount of Jean’s monthly phone bill in terms of m, the number of minutes of long-distance calls she makes. f(m) = 25 + 0.07m How would you write this as an EQUATION? 7 Functional Notation To write an equation in functional notation, we give the function a name, typically a letter such as f, g, or h. Then use an algebraic expression to describe the y-coordinate of an ordered pair. Equation: y = 2x + 16 Functional notation: f(x) = 2x + 16 Equation: m = h – 2 Functional notation: f(h) = h – 2 8 On the TAKS, you will be asked to solve problems in which you must write an equation or inequality for a given situation. Example: Grade 9 TAKS The Alejo family budgeted $2000 for their vacation. Their budget consisted of $800 for travel costs and $75 per day for other expenses. Which inequality represents the number of days, x, the family could have stayed on vacation? A 800 + 75x ≤ 2000 B 800x + 75 ≥ 2000 C 800x – 75 ≥ 2000 D 800 – 75x ≤ 2000 9 Grade 9 TAKS The temperature in degrees Celsius, C, is 5/9 of the difference between the temperature in degrees Fahrenheit, F, and the constant 32. Which equation best represents this relationship? A C = 5/9 – (F + 32) B C = 5/9 (F + 32) C C = 5/9 (F – 32) D C = 5/9 – F + 32 10 Grade 10 TAKS Vicki works as a salesclerk in a clothing store. She earns $10 per hour plus a commission of 6% of her total sales. Which equation represents e, her total earnings, when she works h hours and sells a total of d dollars in merchandise? A e = 10h + 0.06d B e = 10h + 0.6d C e = 6h + 10d D e = 0.06h + 10d 11 Grade 10 TAKS A candy company sells chocolatecovered cherries in a box. The empty box weighs 4.2 ounces. Each piece of candy weighs at least 1.8 ounces. Which inequality best describes the total weight in ounces, w, of a box of chocolate – covered cherries in terms of c, the number of candies in the box? A w ≥ 1.8c + 4.2 B w ≥ 1.8c – 4.2 C w ≥ 4.2c + 1.8 D w ≥ 4.2c – 1.8 12 Grade 11 TAKS Eddie’s Towing company charges 440 to hook a vehicle to the tow truck and $1.70 for each mile the vehicle is towed. Which equation best represents the relationships between the number of miles towed, m, and the total charges, c? A c = 40 + 1.70 B c = 40 + 1.70m C c = 40m + 1.70m D c = 40m + 1.70 13 Grade 11 TAKS An artist studies human proportions in order to make realistic drawings. He observes that a person’s kneeling height, y, is ¾ of the person’s standing height, x. Which equation best represents this relationship? A y=¾x B y=-¾x C y=x-¾ D y=x+¾ 14