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

Warm-UP 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? x = 9 x = 12 x = 600 x = 160 x = 120

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

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

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

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

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

Check whether the given number is a solution of the equation. YES

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

You are in a restaurant and your bill comes to $25 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

Five people want to share equally in the cost of a birthday present 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

Solve for y

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

Warm up Answers 1. 2. 3. 4.

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

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

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

To solve you do the opposite: 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

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

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

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

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

Multiplying by a Reciprocal First…

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

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

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

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

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

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

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%

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

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%

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

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%

Sarah Roderick and Erin 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%

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

Lesson 3.3, For use with pages 148-153 Solve the equation. x 3. 2 3 = 18 ANSWER 27 4. 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. ANSWER 4 h

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

Daily Homework Quiz For use after Lesson 3.2 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. 4. ANSWER y = 3x 9; 1 – 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. 5. ANSWER 11 checks

Solve an equation by combining like terms 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. = 30 5 5x Divide each side by 5. x = 6 Simplify.

EXAMPLE 2 Solve an equation using the distributive property Solve 7x + 2(x + 6) = 39. 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 METHOD 1 METHOD 2 Do Some Steps Mentally 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 = 9x 9 27 x = 3

EXAMPLE 3 Standardized Test Practice SOLUTION 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. ANSWER The correct answer is D. A C D B

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

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

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

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

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

EXAMPLE 4 GUIDED PRACTICE Multiply by a reciprocal to solve an equation for Example 4 Solve the equation. Check your solution. 2 5 (3r + 4) = 10 5. 7 ANSWER

EXAMPLE 4 GUIDED PRACTICE Multiply by a reciprocal to solve an equation for Example 4 Solve the equation. Check your solution. 6. 4 5 (4a – 1) = 28 – –8.5 ANSWER

EXAMPLE 5 Write and solve an equation A flock of cranes migrates from Canada to Texas. The cranes take 14 days (336 hours) to travel 2500 miles. The cranes fly at an average speed of 25 miles per hour. How many hours of the migration are the cranes not flying? BIRD MIGRATION

EXAMPLE 5 Write and solve an equation SOLUTION Let x be the amount of time the cranes are not flying. Then 336 – x is the amount of time the cranes are flying. 2500 = 25 (336 – x)

Write and solve an equation EXAMPLE 5 Write and solve an equation 2500 = 25(336 – x) Write equation. 2500 = 8400 – 25x Distributive property –5900 = –25x Subtract 8400 from each side. 236 = x Divide each side by –25. ANSWER The cranes were not flying for 236 hours of the migration.

EXAMPLE 5 GUIDED PRACTICE Write and solve an equation for Example 5 7. WHAT IF? Suppose the cranes take 12 days (288 hours) to travel the 2500 miles. How many hours of this migration are the cranes not flying? 188 h ANSWER

Try a few on your own. 5z + 16 = 51 14n - 8 = 34 4b + 8 = 10 -2 z = 7