Chapter 3 ReviewReminder: This test is a common assessment!!!

Warm-UPWhat 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

€

x60

=15

100

€

24200

=x

100

€

66x

=11

100

€

x500

=32

100

€

6x

=5

100

Solve.1) 5x + 4 = 39 2) x

34 2

-4 -45x = 355 5x = 7

+4 +4x3

6(3) (3)

x = 18

Solve.

6(x + 4) - 2(x - 7) = 106x + 24 - 2x + 14 = 10

4x + 38 = 10-38 -384x = -284 4x = -7

Solve. 3(x - 2) = 17

3x - 6 = 17+6 +63x = 233 3 x

233

7 23

-(5 - x) = 9-5 + x = 9

+5 +5x = 14

Solve.

Solve these on your own:

€

y3

= −17

19

y =12

€

0 =187

t

−67

x =178

€

42b = 7

−5a = −30

y = -51 t = 0

y = 108

x =

€

−11948

b =

€

16

a = 6

3 3

€

718

•

€

•7

18

Remember: “solve” means isolate the variableMULTIPLY BY THE RECIPRICAL!!!

42 42

b =

€

742

9 9

€

•−76

€

−76

• -5 -5

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

€

2x − x − 23 = −2;7

7x − 6(3 − x) = 26;8

€

56

x + 2 = −8;12

x3

− 4 = 5;27

NO NO

NO YES

€

2(7) − (7) − 23 = −2?

€

56

(12) + 2 = −8?

€

7(8) − 6(3 − 8) = 26?

€

(27)3

− 4 = 5?

Solve each equation if possible.

€

8 − (−3n) = 3n − 2

9.1(1− x) + 5x = −4.2(x − 8)

56

(24 − 36b) =10(2b + 4)

€

3.8y − 4.7 = 3.8y +17.5

−2(a + 5) = 27 − 2a

−9(x − 3) = −(2 − 9x)

€

8 + 3n = 3n − 2-3n -3n

8 = -2NO SOLUTION

€

−4.7 =17.5-3.8y -3.8y

NO SOLUTION

€

9.1− 9.1x + 5x = −4.2x + 33.6

€

9.1 − 4.1x = −4.2x + 33.6

€

9.1+ .1x = 33.6

€

.1x = 24.5

€

x = 245

€

.1x = 24.5

€

−2a −10 = 27 − 2a

−10 = 27 NO SOLUTION

€

20 − 30b = 20b + 40

€

20 = 50b + 40

€

−20 = 50b

b =−25

€

−9x + 27 = −2 + 9x

27 = −2 +18x

29 =18x

x =2918

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??

€

.15(25) = 3.75Then just ADD 3.75 from yourtotal bill.

$25+$3.75 = $28.75

ORWe are increasing by 15%, so thatmeans we are paying 115% of the total bill.

€

1.15(25) = 28.75

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 peoples = each person’s share

€

105.99n

= s

€

105.995

= 21.198

So each person will pay about $21.20

Solve for y

€

5x − 2y = 8

−2x + 3y = 7

€

x = 2y + 9

14x − 7y = 28€

y =52

x − 4

€

y =12

x −92

€

y =23

x +73

€

y = 2x − 4

Warm upSolve the following for the indicated variable:1.

2.

3.

4.

3 8 14x

5 83x

2 4 18x

2( 15) 482x

Warm up Answers1.

2. 3.

4.

2x

18x 9x

5x

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

62104 xx xx 21920

5 2 1 3 2y y y

No Solution

rr 45742

Infinitely Many Solutions

X = 13

Your Turn…Solve the following for the indicated variable:

n = 20

Infinitely many Solutionsx = -7

No Solutions

102

84

x

131238 n

235)1(3 aa

ttt233

25

Steps for Solving….1. Simplify one or both sides of the

equation (if needed).2. 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 SDM A

PES D MA

Solving a Linear Equation86

31

x Write the original equation.66 Subtract 6 from each side.14

31

x Simplify. 14

31

x Multiply each side by

3.42x Simplify. CHECK

3 x x 3

Combining Like Terms First…

24837 xx Write the original equation.2484 x Combine like terms.

88 Add 8 to each side.324 x Simplify.

8x Simplify.CHECK

324 xDivide each side by 4. 4 4

Using the Distributive Property…

28)4(35 xx Write the original equation.

281235 xx Distribute the 3.28128 x Combine like terms.

Subtract from both sides.

2x

Divide both sides.CHECK

1212

Simplify168 x8 88

Simplify.

Distributing a Negative…

21)2(34 xx Write the original equation.

21634 xx Distribute the 3 and the negative.

216 x Combine like terms.Subtract from both sides.

5xCHECK

66

Simplify

Multiplying by a Reciprocal First…

)3(5666 x

Practice…

573

1327

20132

1572

xx

x

x

x

6)2(12

18)2(3

947

x

x

xxx = 4

x = 14

x = 8

x = 3

x = 3/2

x = 8

x = -3

Problem 1Brittany Berrier became a famousskater. She won 85% of her meets. If she had 250 meets in2000, how many did she win?

x = 212.5

Problem 2Krystyl Ferguson workedat the zoo. If 3 of her17 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 manycustomers did he have?

125 total customers

Problem 4

Emily Lower and Jasmine Parks were great WNBAball players. They made $700,000 a year. If they owed22% for taxes, how muchdid they pay in taxes?

$154,000

Problem 5Tiffany Lowery got 65 referralsduring the year. If 14% of these were for tardies,how many times did she getcaught for being tardy? Shedid 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 inJanuary. If he played 35 classicalC.D.’s, what is the percent of classicalC.D.’s he played.

19%

Problem 7

Brett Smith became a doctor.He fixed elephant trunks. He fixed 78.5% of all the elephants hetreated. He fixed 45 elephanttrunks. How many elephants didhe treat in all.

57.32 elephants

Problem 8Ashley Scalf became a famousgolfer. She did occasionally hitone into the pond. If she hit 7 outof 85 hits into the pond, what percentage did she hit into the pond.

8.2%

Problem 9Jeremy Devereaux got thenice guy award. If 42people voted and Jeremygot 85% of the votes, howmany people voted for Jeremy?

35.7 votes

Problem 10

Brad (the Bull) Denton and Daniel (Killer) McFallsjoined the WWE. They won 16 of their 23 bouts. What percentage did they win.

69.6%

Problem 11 Sarah Roderick and ErinLanning became Las Vegasshow girls. If they paid $45,000in taxes and they made $3,000,000 per year, what percentagedid 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

2. 5g – 7 = 58

ANSWER 13

Solve the equation.

Lesson 3.3, For use with pages 148-153

ANSWER

ANSWER 4 h

Solve the equation.x 3. 2

3 = 18

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.

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 termsEXAMPLE 1

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.

= 305

5x5

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 1Show All Steps

7x + 2(x + 6) = 39

7x + 2x + 12 = 39

9x + 12 = 39

9x + 12 – 12 = 39 – 12

9x = 27

x = 3

=9x9

279

METHOD 2Do Some Steps Mentally7x + 2(x + 6) = 39

7x + 2x + 12 = 39

9x + 12 = 39

9x = 27

x = 3

Standardized Test PracticeEXAMPLE 3

ANSWERThe correct answer is D.A C DB

SOLUTIONIn 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.

GUIDED PRACTICE for Examples 1, 2, and 3

9d – 2d + 4 = 321.

Solve the equation. Check your solution.

4ANSWER

EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3

2w + 3(w + 4) = 272.

3ANSWER

Solve the equation. Check your solution.

EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3

6x – 2(x – 5) = 463.

9ANSWER

Solve the equation. Check your solution.

Multiply by a reciprocal to solve an equationEXAMPLE 4

Write original equation.32

(3x + 5) = –24

23

32

(3x + 5) = (–24)23

Multiply each side by , the reciprocal of .

233

2

3x + 5 = –16 Simplify.

3x = –21 Subtract 5 from each side.

x = –7 Divide each side by 3.

32

(3x + 5) = –24Solve .

Multiply by a reciprocal to solve an equation

EXAMPLE 4GUIDED PRACTICE for Example 4

34

(z – 6) = 124.Solve the equation. Check your solution.

22ANSWER

Multiply by a reciprocal to solve an equation

EXAMPLE 4GUIDED PRACTICE for Example 4

25

(3r + 4) = 105.

Solve the equation. Check your solution.

7ANSWER

Multiply by a reciprocal to solve an equationEXAMPLE 4GUIDED PRACTICE for Example 4

6. 45

(4a – 1) = 28–

Solve the equation. Check your solution.

–8.5ANSWER

Write and solve an equation

EXAMPLE 5

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

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.

Write and solve an equation

2500 = 25 (336 – x)

EXAMPLE 5

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.

Write and solve an equation

EXAMPLE 5 Write and solve an equationGUIDED PRACTICE 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 hANSWER

Try a few on your own.5z + 16 = 51

14n - 8 = 34

4b + 8 = 10 -2

z = 7

n = 3

b = -7