9.4 – Problem Solving General Guidelines for Problem Solving 1. Understand the problem. Read the problem carefully. Identify the unknown and select a variable. Construct a drawing if necessary. 2. Translate the information to an equation. 3. Solve the equation and check the solution. 4. Interpret the solution.

Example 1: Three times the difference of a number and 5 is the same as twice the number decreased by 3. Find the number. k is the number Three times The difference of a number and 5 is twice the number decreased by – Problem Solving

Example 1: 9.4 – Problem Solving

Example 1: Check: 9.4 – Problem Solving

Example 2: The difference between two positive integers is 42. One integer is three times as great as the other. Find the integers. x = one integer The difference between two positive integers is42 3x = the other integer 9.4 – Problem Solving

Example 2: Check: 9.4 – Problem Solving

Example 3: A 22-foot pipe is cut into two pieces. The shorter piece is 7 feet shorter than the longer piece. What is the length of the longer piece? Longer piece = m Longer pieceShorter pieceplusis22 feet Shorter piece = m – – Problem Solving

Example 3: 9.4 – Problem Solving

Example 3: Check: 9.4 – Problem Solving

Example 4: A college graduating class is made up of 450 students. There are 206 more females than males. How many males are in the class? Males = h MalesFemalesplusis450 students Females = h – Problem Solving

Example 4: 9.4 – Problem Solving

Example 4: Check: 9.4 – Problem Solving

Example 5: A triangle has three angles A, B, and C. Angle C is 18 degrees greater than angle B. Angle A is 4 times angle B. What is the measure of each angle? plus 9.4 – Problem Solving Reminder: The sum of the angles in a triangle is:

Example 5: 9.4 – Problem Solving

Example 5: Check: Other angles: 9.4 – Problem Solving

9.5 – Formulas and Problem Solving General Guidelines for Solving for a Specific Variable in a Formula 1. Eliminate fractions from the formula. 2. Remove parentheses from the formula using the distributive property. 3. Simplify like terms. 4. Get all terms containing the specified variable on one side of the equation. 5. Use the multiplicative inverse property to get the specified variable’s coefficient to one. 6. Simplify the results if necessary.

Example 1: Using the given values, solve for the variable in each formula that was not assigned a value. Check: 9.5 – Formulas and Problem Solving

Example 2:Volume of a Pyramid 9.5 – Formulas and Problem Solving LCD:3

Example 2:Volume of a Pyramid Check: 9.5 – Formulas and Problem Solving

Example 3: Solve for the requested variable. Area of a Triangle – solve for b 9.5 – Formulas and Problem Solving LCD:2

Example 4: Solve for the requested variable. Celsius to Fahrenheit – solve for C 9.5 – Formulas and Problem Solving LCD:5

Example 4: Solve for the requested variable. Celsius to Fahrenheit – solve for C Alternate Solution 9.5 – Formulas and Problem Solving

Guidelines for Using Formulas in Problem Solving 1. Understand the problem. Read the problem carefully. Identify the known, unknown and the variable(s). Construct a drawing if necessary. 2. Translate the information to a known formula. 3. Solve the equation and check the solution. 4. Interpret the solution. Formulas describe a known relationship among variables. Most formulas are given as equations, so the guidelines for problem solving are relatively the same. 9.5 – Formulas and Problem Solving

Example 1: A pizza shop offers a 2-foot diameter round pizza and a 1.8-foot square pizza for the same price. Which one is the better deal? Round PizzaSquare Pizza 9.5 – Formulas and Problem Solving

Example 2: A certain species of fish requires 1.6 cubic feet of water per fish. What is the maximum number of fish that could be put into a tank that is 3 feet long by 2.4 feet wide by 2 feet deep? Cubic feet is a unit of volume. Volume for FishVolume of Tank Number of fish (f) times Required volume per fish equalslength*width*height f*1.6=3*2.4*2 9.5 – Formulas and Problem Solving

Example 2: 9.5 – Formulas and Problem Solving

9.6 - Linear Inequalities and Problem Solving Properties of Inequality Addition Property of Inequality If a, b, and c are real numbers, then (The property is also true for subtraction.)

Properties of Inequality Multiplication Property of Inequality 1. If a, b, and c are real numbers and c is positive, then 2. If a, b, and c are real numbers and c is negative, then are equivalent inequalities Linear Inequalities and Problem Solving

Graphing an Inequality Linear Inequalities and Problem Solving

Guidelines for Solving a Linear Inequality 1. Eliminate fractions from the formula. 2. Remove parentheses from the formula using the distributive property. 3. Simplify like terms. 4. Get all terms containing the specified variable on one side of the equation using the addition property of inequality. 5. Use the multiplication property of inequality to get the specified variable’s coefficient to one. 6. Simplify the results if necessary Linear Inequalities and Problem Solving *****Reverse the inequality sign when multiplying or dividing by a negative value.*****

Solve each inequality and graph the solution. Example 1: Linear Inequalities and Problem Solving

Solve each inequality and graph the solution. Example 2: Linear Inequalities and Problem Solving

Solve each inequality and graph the solution. Example 3: Linear Inequalities and Problem Solving

Solve each inequality and graph the solution. Example 4: Linear Inequalities and Problem Solving LCD: 21

Example 4: Linear Inequalities and Problem Solving