1. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 9.5 Formulas and Applications

2. 2 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. The area of a rectangle is 35 square feet. If the length is 2 feet more than the width, what are the dimensions of the rectangle? 1. Understand the problem. Draw a sketch. Let w = the width of the rectangle. Continued w Let w + 2 = the length of the rectangle. w + 2 A = lw 2. Write an equation. 35 = w(w + 2) Substitute. Use the formula for the area of a rectangle. Example

3. 3 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. The area of a rectangle is 35 square feet. If the length is 2 feet more than the width, what are the dimensions of the rectangle? 35 = w 2 + 2w Remove parentheses. w 2 + 2w  35 = 0 Write in standard form. 3. Solve and state the answer. 35 = w(w + 2) (w + 7)(w  5) = 0 Factor. w =  7 w = 5 Solve for w. The width of the rectangle is 5 feet and the length is 7 feet. Example (cont)

4. 4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. A class of students wanted to give their teacher a $420 mall gift certificate for her birthday. They agreed to split the cost equally. At the last minute, seven other students wanted to help share the cost. This decreased the amount each student gave by $5. How many students originally planned to give the gift certificate? 1. Understand the problem. Let s = the number of students. Continued Let c = the cost per student in the original group. # of students × cost per student = $420 Example

5. 5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. A class of students wanted to give their teacher a $420 mall gift certificate for her birthday. They agreed to split the cost equally. At the last minute, seven other students wanted to help share the cost. This decreased the amount each student gave by $5. How many students originally planned to give the gift certificate? 2. Write an equation. s · c = 420 Continued If the number of students increases by 7, the cost per student decreases by $5. (s + 7)(c  5) = 420 Example (cont)

6. 6 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. A class of students wanted to give their teacher a $420 mall gift certificate for her birthday. They agreed to split the cost equally. At the last minute, seven other students wanted to help share the cost. This decreased the amount each student gave by $5. How many students originally planned to give the gift certificate? 3. Solve and state the answer. Continued (s + 7)(c  5) = 420 Solve the equation for c. s · c = 420 Substitute. Example (cont)

7. 7 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. A class of students wanted to give their teacher a $420 mall gift certificate for her birthday. They agreed to split the cost equally. At the last minute, seven other students wanted to help share the cost. This decreased the amount each student gave by $5. How many students originally planned to give the gift certificate? Continued Add Multiply each side by s. FOIL. Example (cont)

8. 8 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. A class of students wanted to give their teacher a $420 mall gift certificate for her birthday. They agreed to split the cost equally. At the last minute, seven other students wanted to help share the cost. This decreased the amount each student gave by $5. How many students originally planned to give the gift certificate? Continued Write in standard form. Factor. Solve for s. Example (cont)

9. 9 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. A class of students wanted to give their teacher a $420 mall gift certificate for her birthday. They agreed to split the cost equally. At the last minute, seven other students wanted to help share the cost. This decreased the amount each student gave by $5. How many students originally planned to give the gift certificate? The number of students who originally planned on buying the gift certificate was 21. 4. Check. If the number of students was increased to 28, would the cost per student decrease by $5? 21 students × $20 = 420 28 students × $15 = 420 Example (cont)