Chapter 2

 Key words that indicate you have an equal sign  Is  Is as much as  Is the same as  Is identical to

 Seven times a number squared is five times the difference of k and m  Fifteen times a number subtracted from 80 is 25.  The quotient of a number and 8 increased by 2 is 16.  The product of 27 and k is h squared decreased by 9

 There are approximately 87,000 flights per day in the United States. How many days will it take for 261,000 to have occurred?  There are 50 members in the North Carolina Senate. This is 70 fewer than the number of North Carolina House of representatives. How many members are in the North Carolina House of Representatives?

 Area of a triangle  Perimeter of a rectangle  Volume of a sphere  Surface area of a rectangular prism  The Pythagorean Theorem  Etc….

 6z – 15 =- 45  y 2 + 3x = 4  (3/2)r – t 3 = 132  12 – 2x = (5 + x)/2

 Let t = the time that Maxine drove in each turn  t + 4= the time that Tia drove in each turn  2t + (t+4) = 28  Let m= Max’s salary .1s = Max’s bonus  m +.1m = 525  Let f = cost of fries  f = cost of a burger  4(f ) – f = 8.25

 Whatever you do on one side, you MUST do on the other  INVERSE Operations undo each other  Dividing is the same as multiplying by the reciprocal  The operation to be “undone” is the operation being done on the VARIABLE!

 Simplify  Write the equation with the least amount of variables, numbers, and operations  Undo Addition and Subtraction  Undo Multiplication and Division

 11x – 4 = 29  (a + 7)/8 = 5  12 = -7f – 9  -3 = 2 + a/11  (3/2)a – 8 = 11

 Chris is buying a pair of water skis that are on sale for 2/3 of the original price. After, he uses a $25 gift certificate, the total before tax is $115. What was the original price of the skis?  Len read ¾ of a graphic novel over the weekend. Monday he read 22 more pages. If he had read 220 pages, how many pages does the book have?

 Find three consecutive integers with a sum of 21

 Consecutive Integers  Consecutive Even Integers  Consecutive Odd Integers  n, n+1, n+2, n + 3,…  n, n+2, n+4, ….  n, n + 2, n + 4, …  How can odd and even patterns be the same???

 Find three consecutive odd integers with a sum of -51

 2 + 5k = 3k – 6  x/2 + 1 =( ¼)x – 6  1.3c = 3.3c  6(5m – 3) = 1/3 (24m + 12)  5x + 5 = 3(5x – 4) – 10x  3(2b – 1) – 7 = 6b - 10

 The distance a number is from zero on a number line  Always a positive number  Denoted with n  6  -4  - 8

 Evaluate:  m + 6 – 14, Let m = 4  – 4x, Let x = 2

 f + 5 = 17  b – 1 = -3  3n – 4 = 6

 Means and Extremes  a:b = c:d  a = c b d  Solving Proportions  x = x-2 = x + 4 = 3 5 8

 It takes 7 minutes for Bella to walk around the gym track. At this rate, how many times can she walk around the track in half an hour?  The Ramsey Cascade Trail is about 1 1/8 inches long on a map with scale 3 inches = 10 miles What is the actual length of the trail?

 How many miles long is a 10K race? (1 meter = yards, 1 mile = 1760 yards)  How many square feet = 2000 sq inches?  How many gallons = 920 cups?  How many ft/sec is 25 mi/hour?  How many km/hr is 55 mi/hr?

 P. 119

 Change “over” original!!!  Ex.  Original: 66 New: 30  Original: 24 New: 40  The total number of passengers on cruise ships increased 10% from If there were million passengers in 2009, how many were there in 2007?

 Use the formula for the area of a triangle to solve for the height.  Find the radius for the circumference of a circle.  Solve for m: 4m – 3n = 8  Solve for q: a(q – 8) = 23  Solve for x: 3x – 2y = xz + 5

 Two or more parts are combined into a whole  More than one relationship is contained in the problem  Ex.  Weighted averages (marking period grades, baseball slugging average)  Mixture Problems  Percent Mixture Problems  Uniform Motion Problems

 A tea company sells blended tea for $25 per pound. To make blackberry tea, dried blackberries that cost $10.50 a pound are blended with black tea that costs $35 per pound. How many pounds of black tea should be added to 5 pounds of dried blackberries to make blackberry tea?

 Premium coffee sells for $9.50/ pound, supreme sells for $11.75/pound, and a blend sells for $10.00/pound. How many pounds of Premium coffee beans should be mixed with 2 pounds of Supreme coffee to make the coffee blend?

 Mrs. Matthews has 16 cups of punch that is 3% pineapple juice. She also has a punch that is 33% pineapple juice. How many cups of the 33% punch will she need to add to the 3% punch to obtain a punch that is 20% pineapple juice?

 One type of antifreeze is 40% glycol, and another type of antifreeze is 60% glycol. How much of each kind should be used to make 100 gallons of antifreeze that is 48% glycol?

 Two trains are 550 miles apart heading towards each other on parallel tracks. Train A is traveling east at 35 miles per hour, while train B travels west at 45 miles per hour. When will the trains pass each other?