3-8 HW: Pg. 183-186 # 11-29o, 32-35, 39-42, 50-58e11.)$0.40 per can 13.) about $0.93 per quart

15.) 300 mi/hr 17.) 0.05 mi/min

$1.20 $1.5919.) $0.24 =$0.23 So the $1.59 box is a better buy.

5 721.) 21,000,0

00 /

12 oz 1 cup 123.) =1 , 1.5

8 oz 256 miles 1.609km

25.) =90.1 km 1 mile

15 miles 20 gallons27.) =300 miles

1 gallon

1458829.) 50 =x 50 47=2350 About 2

313

mi wk

c or c

350 more books.

320-288 x 32 x32.) = 3500 = 3500 350 =x

320 3500 320 3500About 350 people have made a phone call.

$2.2533.) =0.16=16%

$14$0.68

34.) =0.06=6% $11.29292

35.) =0.65=65% 450is % 719 71 71x 71900

39.) = = 71x=71900 = x 1013 About 1013 people took the survey.of 100 x 100 71 71

40

.) 83.9%(1400)=0.839(1400)=1175 About 1175 students participate in viewing activies

270 77.2 77.2x 2700041.) = 77.2x=27000 = x = 350 About 350 students were surveyed.

x 100 77.2 77.2

42.) Example: If 299 students participate in social activities, estimate number of students surveyed.

299 74.8 74.8x 29900= 74.8x=29900 = x 400 About 400 students were sur

x 100 74.8 74.8 veyed.

1 150.) -2.4 < 3.2 & 3.2 >-2.4 52.) -1.8 > -2 & -2 < -1.8 54.) -1 1.75& 1.75 1

3 356.) 1.6 58.) 10.92y-16.9=-7.1y-2.8

+7.1y +16.9 +7.1y +16.9

18.02y 14.1 =

18.02 18.02 y = 0.78

Pg. 186 - Quiz 3 # 1 - 12

Turn in to be GRADED!

Warm-Up: 4 minutes to work!1.) You have recorded your car mileage and gasoline use for 5 weeks. Estimate the number of miles you can drive on a full 12-gallon tank of gasoline.

2.) You are visiting Canada and you want to exchange $150 for Canadian dollars. The rate of currency exchange is 1.4 Canadian dollars per United States dollar. How many Canadian dollars will you receive after the exchange?

3.) When you leave Canada to find that you have 15 Canadian dollars left. How many United States dollars would you get back if the rate of currency exchange is now 1.3 Canadian dollars per U.S. dollar?

4.) About 74% of water used in houses is used in bathrooms, about 5% in kitchens, and about 21% in other places. About 9 gallons are used in the kitchen each day. Estimate the total gallons used each day.

Number of Miles

Number of Gallons

159 5.0

237 6.9

195 6.0

215 6.5

183 5.7

159+237+195+215+183 miles 9891.)

5 6.9 6 6.5 5.7 gallons 30.1

32.9 miles = 394.8 miles for a 12 gallon tank

ga(12 gallons

n)

llo

2.) $150 US1.4 Canadian dollars

$1 US

210 Canadian dollars

3.) 15 Canadian dollars$1 US

1.3 Canadian dollars

11.5385 = $11.54 US

9 gallons 9 gallons4.) 5% = x (.05) =

x total gallons x total gallons(x)

.05x 9 x = 180 total gallons

.05 .05

Find your partnerFind your partner

Complete the sticky note problem attached to your worksheet and find the person who got the same answer as you.

That person is your partner for the next activity!

Partner Problem – Partner Problem – 10 min. to work!Ron the realtor is offered a job directly out of real-estate school. He has a choice as to

which way he will receive his salary the first year.Salary Plan 1: Base pay of $2000 per month plus a 3% commission on each sale.Salary Plan 2: No base pay but a 6% commission on each sale.

a.) If Ron averages $45,000 in sales per month, how much would he earn under the FIRST plan? How much under the SECOND plan? Which is the better choice in this case? EXPLAIN!

b.) Write a verbal model for Salary Plan 1 that relates base pay, total pay, sales in a month, and percent commission.

c.) Write a verbal model for Salary Plan 2 relating sales in a month, percent commission, and total pay.

d.) Write an equation to determine when it would be better to switch from the first plan to the second plan. Give a one- or two-sentence answer that includes Ron’s sales in a month. Round to the nearest dollar, if necessary.

e.) Ron makes a goal to earn $8000 every month. State which choice he should select and EXPLAIN your reasoning. Use the verbal model from (b) or (c) to set up an equation and determine what his sales should be to achieve his goal.

Daily HW Quiz/Partner Problem AnswersDaily HW Quiz/Partner Problem Answers

2n. d) p1st lan:plan: 4 45000(5000(0.03) + 200 0.06) = $270

Better

0 = 135

choice

0 + 2000 =

is the 1s

$335

t p

00

lan.

a

total pay = base pay + percent commission (sales in a mob.) nth)

total pay = percent commission (sales in a moc.) nth)

2nd plan: (0.06)x = 8000

1st plan: 2000 + (0.03)x = 8000 0.e.)

If Ron wants

03x = 6000 x = 20

to earn $8000 a mon

0,000

th, th

x = 133,

en he sho

333 sa

uld se

le

le

s

c

sales

t the because he would have

to sell less per

2nd

mon

plan

th.

d.) x = monthly sales, =

- 0.03x -0.03x

2000 = 0.03x

2000 + 0.0

0.0

6x 3x

0.03 0.03 66667 x

If Ron's sales are $66,667 a month than both p If he had sales

MORE than $66,667

lans would pay the same amount.

, then the 2nd plan would pa

y mor

If he had sales LESS than $66,667,

then the 1st plan would pay m

e.

ore.

Concept Review• Solving equations using one operation

- Use OPPOSITE OPERATIONS to isolate the variable

• Solving multi-step equations- Use OPPOSITE OPERATIONS to isolate the variable in more than 1 step

• Solving equations with variables on both sides- Move your variable to one side and the numbers to to the other side using OPPOSITE OPERATIONS- Either get 1 answer, a FALSE statement or NO SOLUTION, or a TRUE statement or ALL REAL #S

Concept Review Continued• Linear equations and problem solving

- Draw a picture, label a diagram then write an equation to solve the word problem- Answer each word problem in a SENTENCE!

• Formulas and Functions- Isolate the variable you want to solve for- “Solve for --- in terms of ---” means to solve for the variable listed first

• Rates, ratios, and percents- Find a unit rate – DIVIDE- Ratios are fractions that need to be simplified- Percent = out of 100, move the decimal point TWO places to the left

PracticeSolve the equation if possible and SHOW WORK on BOTH sides

of the equation. Do 3 problems: 1 from #1-3, 1 from #4-6, and 1 from #7+8 x

1.) 19 = a - 4 2.) 5 3.) -3y = -184

4.) 17 = 5 - 3p 5.) -3(x-2) = x 6.) 7x - 3x - 8 = 24

7.) x - 2x + 3

= 3 - x 8.) 5x +24 = 5(x - 5)

x1.) 19 = a - 4 2.) 4 5 4 3.) -3y = -18

4 + 4 + 4 x = 20 -3 -3

23 = a

y = 6

4.) 17 = 5 - 3p 5.) -3(x-2) = x 6.) 7x - 3x - 8 = 24

- 5 - 5 -3x + 6 = x 4x - 8 = 24

12 = -3p +3x +3x +8 +8

-3 -3 6 = 4x 4x = 32

-4 = p 4 4 4 4

3 x

2 x = 8

7.) x - 2x + 3 = 3 - x 8.) 5x + 24 = 5(x - 5)

- x + 3 = 3 - x 5x + 24 = 5x - 25

+x +x -5x -5x

3 = 3 TRUE, so All real numbers 24 = -25 FALSE, so No Solution

For # 9 – 10, write and solve an equation to answer each word problem.9.) Currently, you have $60 and your sister has $135. You decide to SAVE $5 of your allowance each week, while your sister decides to SPEND her whole allowance plus $10 per week. How long will it be before you have as much money as your sister?

9.) 60 + 5x = 135 - 10x

+ 10x +10x

15x = 75

15 15 x = 5 It will take 5 weeks until you have as much as your si

-60 -60

ster.1

10.) YEARBOOK DESIGN A page of your school yearbook is 8 inches by 11 inches. 2

3 7The left margin is inch and the space to the right of the pictures is 2 inches. The

4 83

space between pictures is 1

inch. How wide can each picture be to fit three across the 6

width of the page? (Start by labeling the picture)

3 1 17 1 9 110.) + + + + + 8 3x + 4 = 3x =

4 2 2 3 2 33 1

x= Each picture is 1

3 3+

16

inches wide.2

1x x x

7

8

2

62

For # 11 – 14, solve for the indicated variable. Do 2 problems: 1 from #11 or 12, 1 from #13 or 14.

2

11.) C = 2 r, solve for r

112.) V = r h, solve for h

3

13.) 9 - y = 3x, solve so y is a function of x

14.) 2x + 4y - 6 = 0, solve so x is a function of y. Then use the result to find x

when y = -2, -1, 0, and 1.

11.) C = r

2 2

C = 2

2

r

14.)

-4y +6 -4y +6

2x = -4y + 6 y : -2 -1 0 1

2 2 2 so x = -2

2x

x +

+ 4y - 6 = 0

3 x:

7 5 3 1

13.)

-9 -9

-y = 3x - 9 so y

9 - y

= -3x

= 3x

+ 9

2

2 2

2

2

12.) 3 3 3V = r h 3V = h

r

1V

r r

= r h3

For # 15 – 14, write and solve an equation to answer the question.15.) You stuffed 108 envelopes in 45 minutes for your aunt’s

wedding. At this rate, how many envelopes can you stuff in 2 hours?

16.) While visiting Italy you want to exchange $120 for liras. The rate of currency exchange is 1850 liras per United States dollar. How many liras will you receive?

17.) You received a $9 tip from customers who had a bill of $56. What percent tip did you receive?

108 envelopes 108 envelopes15.)

45 minutes 2 hours 45 minutes 120 120

minutes

x x 120

x = 288 envelopes in 288 h ours

1850 liras16.) 120 US$ 222,000 liras

1 US$

917.) 0.1607 = 16% tip

56

Summary• EXPLAIN how to solve equations using one operation

– Ans: UNDO the operation using OPPOSITE operations• EXPLAIN how to solve multi-step equations

– Ans: UNDO the operation using OPPOSITE operations in two or more steps

• EXPLAIN how to solve equations with variables on both sides– Ans: get your variable on one side and the #s on the other using

OPPOSITE operations• EXPLAIN how to solve linear equations in word problems

– Ans: draw a picture or label a diagram, write an equation, then solve the equation, answering the problem in a SENTENCE

• EXPLAIN how to solve formulas for a different variable– Ans: isolate the variable you are looking for by using OPPOSITE

operations• EXPLAIN how to solve problems “y as a function of x”

– Ans: solve for Y using OPPOSITE operations on BOTH sides of the equation

• EXPLAIN how to find unit rates and ratios– Ans: Divide so 1 is in the denominator

• EXPLAIN how to solve problems involving percents– Ans: Set up the equation: % as a decimal = part DIVIDED by whole

Check Yourself

Pg. 190-192 # 2-34e