Ch 7 – The Basic Concepts of Algebra 7.2 – Applications of Linear Equations Synonyms for ADDITION: VERBAL SUM of a number and 3 4 MORE THAN a number A number PLUS 9 2 ADDED TO a number A number INCREASED BY 3 MATHEMATICAL x+3 x+4 x+9 x+2 x+3 Synonyms for SUBTRACTION: VERBAL DIFFERENCE of a number and 3 4 LESS THAN a number A number MINUS 9 A number DECREASED BY 3 MATHEMATICAL x–3 x–4 x–9 x–3 Synonyms for MULTIPLICATION: VERBAL PRODUCT of a number and 3 4 TIMES a number 2/3 OF a number 24% OF a number TWICE a number MATHEMATICAL 3x 4x 2/3x .24x 2x Synonyms for DIVISION: VERBAL QUOTIENT of a number and 3 4 DIVDED BY a number The RATIO of 8 and a number MATHEMATICAL x/3 4/x 8/x Synonyms for “EQUAL”: VERBAL 3 plus a number IS 10 4 minus a number IS GREATER THAN 8 The product of 5 and a number IS LESS THAN 100 MATHEMATICAL 3 + x = 10 4–x>8 5x < 100 Let’s try writing verbal phrases as mathematical expressions! 1. The product of a number and 12 is decreased by 7. 2. The sum of a number and 2 is multiplied by 5. Let’s try writing verbal phrases as mathematical expressions! 3. The quotient of a number and 3 is 30. 4. Twice the difference of 12 and a number is less than 142. What is the difference of the phrases below? Write a mathematical model for each. 7 less than a number is 9. 2. 7 and the sum of a number is less than 9 1. NBA Record In 2004 – 2005 NBA regular season, the Phoenix Suns won two more than three times as many games as they lost. The Suns played 82 games. How many wins and losses did the team have? U.S. Senate During the 109th Congress (2005 – 2006), the U.S. Senate had a total of 99 Democrats and Republicans. There were 11 more Republicans than Democrats. How many Democrats and Republicans were there in the Senate? Chemical Mixture How much pure acid is in 250 milliliters of a 14% acid solution? Interest Earned I = Prt If $10,000 is invested for one year at a 3.5% simple interest, how much interest is earned? How much money do you have total? If $550 is invested at a simple interest rate of 4%, how long would you have to keep your money in the bank until you have earned $264 in interest? In a chemistry class, 12 liters of a 12% alcohol solution must be mixed with a 20% solution to get a 14% solution. How many liters of the 20% solution are needed? A chemist must mix 8 liters of a 40% acid solution with some 70% acid solution to obtain a 50% solution. How much of the 70% solution is needed? Coin Mixture A box of coins currently has 44 coins, consisting of pennies, dimes and quarters. The number of pennies is equal to the number of dimes. The total value in the box is $4.37. How many of each denomination are in the box? Distance between Cities A driver averaged 53 miles per hour and took 10 hours to travel from Memphis to Chicago. What is the distance between Memphis to Chicago? Attendance at a School Play The school production of Hamlet was a big success. For opening night, 410 tickets were sold. Students paid $3 each and nonstudents paid $7 each. If a total of $1650 was collected, how many students and how many nonstudents attended? Movie Ticket Prices A movie theater has two ticket prices: $8 for adults and $5 for children. If the box office took in $4116 from the sale of 600 tickets, how many tickets of each kind were sold? 2004 Olympic Results Joanna Hayes of USA ran the 100-m hurdles in 12.37 seconds. What was her rate? Jeremy Warner of USA ran the 400-m run in 44.00 seconds. What was his rate? Partner Activity Each group will make up a word problem about the following topics/formulas. d = rt I = Prt A problem with 2 unknowns (i.e. the Democrat/Republican problem from yesterday or the Movie Ticket prices today) – NO,YOU CAN NOT USE ANY OF THE SAME SINARIOS DONE IN CLASS! You must write out the problem and provide a correct solution. My favorite ones will be used on the quiz next week!