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  Note comparisons, totals, equals, etc. 2. Define Variable(s) and Unknowns  x = ?  Represent other unknowns using x 3. Develop a Plan  Formula  Sentence 4. Write an equation from your plan and Solve equation 5. Answer Question

Examples: 1) The sum of two numbers is 83. One of the numbers is 11 more than the other. What are the numbers?  Define Variable: Let x = number x + 11 = other number  Develop Plan: Number + Other number = Sum  Write 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

1 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

2 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 1st + 2nd + 3rd + 4th Plan: = average 4

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

3 9) The width of a rectangular greenhouse is a 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 AREA of the triangle. x = height of triangle x + 1 =one side x + 2 = base x + 3 = other side

Plan 1: Plan 2:

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

4 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 =

2 14) When of a number is subtracted from 12, the result is 10. Find the number. 3 x = the number 2 Plan: Twelve - of number = 10 3

5 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 tax the motel must pay? x = = tax Plan: Room charges + tax = total receipts