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Chapter 3 Review

Chapter 3 Review . Reminder: This test is a common assessment!!!. Warm-UP. x = 9 x = 12 x = 600 x = 160 x = 120. What number is 15% of 60? 24 is what percent of 200?  66 is 11 % of what number?  What number is 32% of 500?  6 is 5% of what number?. Solve . 2).

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Chapter 3 Review

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  1. Chapter 3 Review Reminder: This test is a common assessment!!!

  2. Warm-UP x = 9 x = 12 x = 600 x = 160 x = 120 • What number is 15% of 60? • 24 is what percent of 200?  • 66 is 11 % of what number?  • What number is 32% of 500?  • 6 is 5% of what number?

  3. Solve. 2) 1) 5x + 4 = 39 -4 -4 +4 +4 5x = 35 5 5 (3) (3) x = 7 x = 18

  4. Solve. 6(x + 4) - 2(x - 7) = 10 6x + 24 - 2x + 14 = 10 4x + 38 = 10 -38 -38 4x =-28 4 4 x =-7

  5. Solve. 3(x - 2) = 17 3x - 6 = 17 +6 +6 3x = 23 3 3

  6. Solve. -(5 - x) = 9 -5 + x = 9 +5 +5 x = 14

  7. Solve these on your own: Remember: “solve” means isolate the variable MULTIPLY BY THE RECIPRICAL!!! 3 3 42 42 y = -51 t = 0 b = b = 9 9 -5 -5 x = a = 6 y = 108

  8. Check whether the given number is a solution of the equation. NO NO NO YES

  9. Solve each equation if possible. -3.8y -3.8y -3n -3n 8 = -2 NO SOLUTION NO SOLUTION NO SOLUTION

  10. You are in a restaurant and your bill comes to $25. You want to leave a 15% tip. What is your total bill? TWO WAYS OF DOING THIS PROBLEM…1 ANSWER!!!! What is 15% of $25?? We are increasing by 15%, so that means we are paying 115% of the total bill. OR Then just ADD 3.75 from your total bill. $25+$3.75 = $28.75

  11. Five people want to share equally in the cost of a birthday present. The present costs $105.99. How much does each person pay? Make an equation to use first! n = number of people s = each person’s share 21.198 So each person will pay about $21.20

  12. Solve for y

  13. Warm up Solve the following for the indicated variable: 1. 2. 3. 4.

  14. Warm up Answers 1. 2. 3. 4.

  15. There are actually three different possible outcomes when solving for a variable. 1. One solution 2. No Solutions 3. Infinitely Many Solutions

  16. Let’s try some examples… Solve the following for the indicated variable: x = -8 X = No Solution Infinitely Many Solutions

  17. Your Turn… Solve the following for the indicated variable: Infinitely many Solutions x = -7 n = 20 No Solutions

  18. Steps for Solving…. • Simplify one or both sides of the equation (if needed). • Use inverse operations to isolate the variable. (DO THE OPPOSITE OF ORDER OF OPERATIONS) To simplify you use: To solve you do the opposite: P E M D A S S A D M E P

  19. 3 x x 3 Solving a Linear Equation Write the original equation. Subtract 6 from each side. Simplify. Multiply each side by 3. Simplify. CHECK

  20. Combining Like Terms First… Write the original equation. Combine like terms. Add 8 to each side. Simplify. 4 4 Divide each side by 4. Simplify. CHECK

  21. Using the Distributive Property… Write the original equation. Distribute the 3. Combine like terms. Subtract from both sides. Simplify Divide both sides. CHECK Simplify.

  22. Distributing a Negative… Write the original equation. Distribute the 3 and the negative. Combine like terms. Subtract from both sides. Simplify CHECK

  23. Multiplying by a Reciprocal First…

  24. Practice… x = 4 x = -3 x = 14 x = 8 x = 8 x = 3/2 x = 3

  25. Problem 1 Brittany Berrier became a famous skater. She won 85% of her meets. If she had 250 meets in 2000, how many did she win? x = 212.5

  26. Problem 2 Krystyl Ferguson worked at the zoo. If 3 of her 17 baboons were sick, What % were sick? 18%

  27. Problem 3 Matt Debord worked as a produce manager for Walmart. If 35 people bought green peppers and this was 28% of the total customers, how many customers did he have? 125 total customers

  28. Problem 4 Emily Lower and Jasmine Parks were great WNBA ball players. They made $700,000 a year. If they owed 22% for taxes, how much did they pay in taxes? $154,000

  29. Problem 5 Tiffany Lowery got 65 referrals during the year. If 14% of these were for tardies, how many times did she get caught for being tardy? She did not get caught every time!! 9.1 tardies

  30. Problem 6 Brett Mull became a famous D.J. He played a total of 185 C.D’s in January. If he played 35 classical C.D.’s, what is the percent of classical C.D.’s he played. 19%

  31. Problem 7 Brett Smith became a doctor. He fixed elephant trunks. He fixed 78.5% of all the elephants he treated. He fixed 45 elephant trunks. How many elephants did he treat in all. 57.32 elephants

  32. Problem 8 Ashley Scalf became a famous golfer. She did occasionally hit one into the pond. If she hit 7 out of 85 hits into the pond, what percentage did she hit into the pond. 8.2%

  33. Problem 9 Jeremy Devereaux got the nice guy award. If 42 people voted and Jeremy got 85% of the votes, how many people voted for Jeremy? 35.7 votes

  34. Problem 10 Brad (the Bull) Denton and Daniel (Killer) McFalls joined the WWE. They won 16 of their 23 bouts. What percentage did they win. 69.6%

  35. Problem 11 Sarah Roderick and Erin Lanning became Las Vegas show girls. If they paid $45,000 in taxes and they made $3,000, 000 per year, what percentage did they pay in taxes? 1.5%

  36. Lesson 3.3, For use with pages 148-153 1. Simplify the expression 9x + 2(x – 1) + 7. 11x + 5 ANSWER Solve the equation. 2. 5g– 7= 58 13 ANSWER

  37. 2 x 3. = 18 3 A surf shop charges $85 for surfing lessons and $35 per hour to rent a surfboard. Anna paid $225. Find the number of hours she spent surfing. 4. Lesson 3.3, For use with pages 148-153 Solve the equation. ANSWER 27 ANSWER 4 h

  38. a 4 1.+ 6 = –14 ANSWER – 80 ANSWER 3 – 3. 36 = 7y 2y + – 4 ANSWER Daily Homework Quiz For use after Lesson 3.2 Solve the equation. 2. 6r – 12 = 6

  39. 4. The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is –6. ANSWER 5. A bank charges $5.00 per month plus $.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month. y = 3x 9; 1 – ANSWER 11 checks Daily Homework Quiz For use after Lesson 3.2

  40. 30 5x = 5 5 EXAMPLE 1 Solve an equation by combining like terms Solve 8x – 3x – 10 = 20. 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – 10 + 10= 20 + 10 Add 10 to each side. 5x = 30 Simplify. Divide each side by 5. x = 6 Simplify.

  41. SOLUTION When solving an equation, you may feel comfortable doing some steps mentally. Method 2 shows a solution where some steps are done mentally. EXAMPLE 2 Solve an equation using the distributive property Solve 7x +2(x + 6) = 39.

  42. METHOD2 Do Some Steps Mentally = 9x 27 9 9 EXAMPLE 2 METHOD1 Show All Steps 7x + 2(x + 6) = 39 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x + 12 = 39 9x + 12 – 12= 39 – 12 9x = 27 9x = 27 x = 3 x =3

  43. SOLUTION ANSWER In Step 2, the distributive property is used to simplify the left side of the equation. Because –4(x– 3) = –4x + 12, Step 2 should be 5x – 4x + 12 = 17. The correct answer is D. A B C D EXAMPLE 3 Standardized Test Practice

  44. 1. 9d – 2d + 4 = 32 ANSWER 4 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the equation. Check your solution.

  45. 2. 2w + 3(w + 4) = 27 ANSWER 3 EXAMPLE 2 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the equation. Check your solution.

  46. 6x – 2(x – 5) = 46 3. ANSWER 9 EXAMPLE 2 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the equation. Check your solution.

  47. 3 Solve . (3x + 5) = –24 2 (3x + 5) = –24 2 (3x + 5) = (–24) Multiply each side by , the reciprocal of. 3 3 2 3 2 3 2 2 3 3 2 EXAMPLE 4 Multiply by a reciprocal to solve an equation Write original equation. 3x + 5 = –16 Simplify. 3x = –21 Subtract 5 from each side. x = –7 Divide each side by 3.

  48. 4. (z – 6) = 12 ANSWER 22 3 4 EXAMPLE 4 for Example 4 Multiply by a reciprocal to solve an equation GUIDED PRACTICE Solve the equation. Check your solution.

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