Math 2303 Section 5.7 Section 5.7 Solving Problems Using Quadratic Equation General strategy for solving word problems: 1. Read the problem carefully and make note of what information is given and what information is given and what is unknown. 2. Pick a variable to represent the unknown quantity. 3. From the given information, determine a quadratic equation for which the unknown quantity is a solution. (For geometry problems, it is helpful to draw a picture). 4. Solve for unknown quantity. Example 1: A company models its annual profits using the function: 20
300 , where P represents profits and x gives the number of units sold. One year, their profits were $167, 700. How many units of their products did they sell? Example 2: The sum of 2 numbers is 21 and their product is 90. What are the two numbers? 1 Math 2303 Section 5.7 Popper 19 question 1: The sum of two numbers is 23 and their product is 132. Find the larger of the two numbers. A. 12 B. 14 C. 16 D. 22 Example 3: A homeowner wants to install a deck around her swimming pool. The swimming pool is a rectangle and measures 25 feet by 32 feet. The deck is to have the same width all the way around the pool. What should be the width of the deck if she has 310 square feet of decking material? Example 4: The length of a rectangular garden is 3 feet less than twice the width. If the area of the garden is 54 square feet, find the width? 2 Math 2303 Section 5.7 Popper 19 question 2: The length of a rectangle is 5 feet more than the width. If the area of the rectangle is 36 square feet, find the width of the rectangle? A. 4 feet B. 9 feet C. 5 feet D. Need more information Example 5: The perimeter of a rectangle is 50 cm and if the area is 144 square centimeters, find the dimensions of the rectangle. Example 6: The height of a triangle is 3 inches shorter than the base. Find the base and height of the triangle if the area of the triangle is 20 square inches. 3 Math 2303 Section 5.7 Use for Popper 19 questions 3, 4 and 5: The base of a triangle is 5 feet longer than the height. Find the base and height if the area of the triangle is 42 square feet. Popper 19 question 3: If x is height then how is the base defined in terms of x? A. 5 B. 5 C. 5 Popper 19 question 4: What is the length height? A. 12 feet B. 7 feet C. 6 feet D. 13 feet Popper 19 question 5: What is the length base? A. 12 feet B. 7 feet C. 6 feet D. 13 feet Solution to Popper 17: Popper 17 question 1: Factor: 2
3
3
a. 8 b. 24 8 c. 4
6 d. 4
6 Popper 17 question 2: Factor : 9
36. a. 3
18 3
6 3
6 b. 3
18 c. 9
9
4 d. 9
1
5 d. 1
9 5
Popper 17 question 3: Solve for x: a. 1
4 b. 1
4 4 c. 1
5 4 Math 2303 Section 5.7 Popper 17 question 4: Solve for x: 4
2
a. 2 b. 100
4
0 4 c. 5
5 d. 10
10 11
Popper 17 question 5: Solve for x: 2
1
a.
4 b. 1
6 4 c. 2
d. 6
Solutions to Popper 18: Popper 18 question 1: Solve for x: A. B. C. D. Popper 18 question 2: Solve for x: 4
A. B. D. 3
49 C. Popper 18 question 3: Solve for x: 4
2
0 A. √ B. √
C. √ D. √
Popper 18 question 4: If the discriminate is equal to zero what does that mean? A. No solution B. Two solutions C. One Real Solution D. Complex Number Popper 18 question 5: If asked to solve for x: 4
0. What is your first step to make this problem easier to solve. A. Put the values for a, b and c in the quadratic formula B. Multiply by the LCD 5