Using Equations to Solve Word Problems Section 2.6 Using Equations to Solve Word Problems

Solving Word Problems Understand the problem. a.) Read the problem carefully to get an overview. b.) Determine what information you will need to solve the problem. c.) Draw a sketch. Label what is known. Determine what is to be found. d.) Choose a variable to represent one unknown quantity. e.) If necessary, represent other unknown quantities in terms of that very same variable. Write an equation. a.) Look for key words to help translate the words into algebraic symbols and expressions. b.) Use a given relationship in the problem or an appropriate formula to write an equation. Solve and state the answer. Check. a.) Check the solution in the original equation. Is the answer reasonable. b.) Be sure the solution to the equation answers the question in the word problem.

Example Twelve more than a number is seventy-two. What is the number? 1. Understand the problem. Let x = the unknown number. 2. Write an equation. x + 12 72 Twelve more than a number is seventy-two x + 12 = 72

Example (cont) Twelve more than a number is seventy-two. What is the number? 3. Solve and state the answer. x + 12 = 72 x = 60 The number is 60. 4. Check. x + 12 = 72 (60) + 12 = 72 72 = 72 

the sum of a number and four Example Six less than one-third of the sum of a number and four is negative two. 1. Understand the problem. Let n = the unknown number. 2. Write an equation. 2 one-third of six less than is negative two = 2 the sum of a number and four

Example (cont) Six less than one-third of the sum of a number and four is negative two. 3. Solve and state the answer. The number is 8. Multiply each side by 3. Combine like terms. Combine like terms.

Example (cont) Six less than one-third of the sum of a number and four is negative two. 4. Check. 

Example A golf course in Florida has a perimeter of 92 miles. The course is in the shape of a rectangle. The length of the course is 30 miles less than triple the width of the course. Find the length and the width of the golf course. 1. Understand the problem. Let w = the width of the course. Let 3w – 30 = the length of the course. To find the perimeter, use the formula: P = 2w + 2l

Example (cont) A golf course in Florida has a perimeter of 92 miles. The course is in the shape of a rectangle. The length of the course is 30 miles less than triple the width of the course. Find the length and the width of the golf course. 2. Write an equation. 2w + 2l = 92 2(w) +2(3w – 30) = 92

Example (cont) A golf course in Florida has a perimeter of 92 miles. The course is in the shape of a rectangle. The length of the course is 30 miles less than triple the width of the course. Find the length and the width of the golf course. 3. Solve and state the answer. 2(w) +2(3w – 30) = 92 2w + 6w – 60 = 92 8w – 60 = 92 8w = 152 w = 19 The width is 19 miles. The length is 3w – 30 = 3(19) – 30; 27 miles

Example (cont) A golf course in Florida has a perimeter of 92 miles. The course is in the shape of a rectangle. The length of the course is 30 miles less than triple the width of the course. Find the length and the width of the golf course. 4. Check. 2w +2l = 92 2(19) +2(27) = 92 38 + 54 = 92 

Example The Langston Coliseum has a total of 800 seats. The balcony level holds the fewest seats. The main floor level has 180 more seats than the balcony level. The orchestra level has 60 seats fewer than twice the number in the balcony level. How many seats are in each level? 1. Understand the problem. Let b = the number of seats in the balcony level Let b + 180 = the number of seats in the main floor level Let 2b – 60 = the number of seats in the orchestra level There are 800 total seats in the Coliseum. Add the number of seats in each section to find the total number.

Example (cont) The Langston Coliseum has a total of 800 seats. The balcony level holds the fewest seats. The main floor level has 180 more seats than the balcony level. The orchestra level has 60 seats fewer than twice the number in the balcony level. How many seats are in each level? 2. Write an equation. b + b + 180 + 2b – 60 = 800 3. Solve and state the answer. 4b + 120 = 800 4b = 680 b = 170

Example (cont) The Langston Coliseum has a total of 800 seats. The balcony level holds the fewest seats. The main floor level has 180 more seats than the balcony level. The orchestra level has 60 seats fewer than twice the number in the balcony level. How many seats are in each level? b = 170 There are 170 balcony seats, 170 + 180 = 350 main floor seats, and 2(170) – 60 = 280 orchestra level seats in the Coliseum. 4. Check 170 + 170 + 180 + 2(170) – 60 = 800 

Example A teacher told Melinda that she has a course average of 78 based on her six math tests. When she got home, Melinda found five of her tests. She had scores of 87, 63, 79, 71, and 95 on the five tests. She could not find her sixth test. What score did she obtain on that test? The average of the six tests is a 78.

Example (cont) A teacher told Melinda that she has a course average of 78 based on her six math tests. When she got home, Melinda found five of her tests. She had scores of 87, 63, 79, 71, and 95 on the five tests. She could not find her sixth test. What score did she obtain on that test? Melinda scored a 73 on the sixth test. This answer checks.