1 Lessons 5 and 6, Section 1.4 5-Step Process for Solving Problems 1. Evaluate the Problem • Draw a Picture • Fill in information in a table • Identify comparisons, totals, equals, etc. 2. Define Variable(s) and Unknowns • x = ? • Represent other unknowns using x 3. Develop a Plan • Write a Formula • Write a Word Sentence 4. Write an equation from your plan and Solve equation 5. Answer Question (with correct labels) Examples: 1) The sum of two numbers is 83. One of the numbers is 11 more than the other. What are the numbers? • Variable: Let x = number x + 11 = other number • Plan: Number + Other number = Sum • Equation: 2) A paddleboat can run 8 miles per hour in still water and the river flows at 3 mph. How long will it take the boat to go 3 miles upstream? How long will it take the boat to go 3 miles downstream? Note: rate upstream = boat – current, rate downstream = boat + current • Variable: t = time • Plan: d = rt Emphasize deriving the equations for each applied problem.2 3) The second angle of a triangle is 5 degrees less than the first angle. The third angle is triple the second angle . Find the measurement of the smallest angle. x = 1st angle = 2nd angle = 3rd angle Plan: Angle 1 + Angle 2 + Angle 3 totals 180 degrees 4) QVC shopping determines the selling price of a diamonique ring by marking up the wholesale price by 25% and adding $4.25 for shipping and handling. If a customer is charged $166.75 for the ring, how much was the wholesale price? x = wholesale price = markup Plan: Wholesale price + Markup + Shipping/handling = Selling price 5) Find three consecutive odd integers such that the sum of the largest, twice the middle, and 3 times the smallest is 50. x = 1st odd integer x + 2 = 2nd odd integer = 3rd odd integer Plan: Largest + Twice middle (2nd) + 3 times smallest (1st) = sum Let the angle that the least is known about equal x . The sum of 3 angles inside of a triangle is always 180° Three consecutive numbers could be represented as x, x + 1, and x + 2. Three consecutive evens or 3 consecutive odds would be represented as x, x + 2, and x + 4; since the smallest to the middle has a difference of 2 and the middle to the largest has a difference of 2.3 6) A piece of wire 100 centimeters long is to be cut into 2 pieces and each piece is to be bent to make a square. The length of each side of the larger square is 1 cm more than the length of each side of the smaller square. What are the dimensions of each square? x = length of side of the smaller square x + 1 = length of side of the larger square Plan: Perimeter smaller + Perimeter larger = 100 7) Lynn wants to have an average of 80 points on his algebra exams. His first three exams are 91, 72, and 81 points. What does he need on his fourth exam to keep his average of 80? x = score on 4th exam Plan: 1st 2nd 3rd 4thaverage4+ + += 8) Julie and Paige have won a total of 43 tennis matches this summer. If Julie won 11 more matches than Paige, how many matches did Julie win? x = wins for ? Plan: wins for Julie + wins for Paige = total matches Perimeter is the distance (length) around a shape. The formula for perimeter of a square is p = 4s, where s is the length of a side.4 9) The width of a rectangular greenhouse is one-fourth its length and its perimeter is 130 meters. Find the length and width of the greenhouse. Variable: Plan: Perimeter = twice width + twice length 10) The height and sides of a triangle are 4 consecutive integers with the height being the smallest integer and the base the third integer. If the perimeter of the triangle is 30 inches, find the length of the longest side of the triangle. x = height of triangle x + 1 =one side x + 2 = base x + 3 = other side Plan: 11) In 2002 there were 301 long distance area codes in the United States. This was an increase of 250% over the number when the area code plan originated in 1947. How many area codes were there in 1947? x = number of area codes in 1947 Plan: Number in 1947 + Increase = Number in 2002 The formula for perimeter of a rectangle is p = 2w + 2L x x+1 x+3 x+25 12) The John Hancock Center in Chicago has a rectangular base whose length measures 65 feet less than twice the width. If the perimeter of the base is 860 feet, what is the length of the base? 13) The two companies with top revenues in the Fortune 500 list for 2002 were Wal- Mart and Exxon Mobil. Their revenues together totaled $412 million. Exxon Mobil revenues were $28 million less than Wal-Mart revenues. What were the revenues for Exxon Mobil? x = 14) When 32 of a number is subtracted from 12, the result is 10. Find the number. x = the number Plan: Twelve - 32 of number = 106 15) At the end of a day, Jeff found that the total cash register receipts at the motel where he works accounted to $2725. This included a 9% sales tax charged. Find the amount of the room charge? x = = tax Plan: Room charges + tax = total
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