BLAST FROM THE PAST

POD Wednesday, 1/15/13

1. Change to a decimal.

2. Johnny wants to be able to bake enough cookies for the bake sale. He has already baked 50 cookies and plans to bake 30 more cookies every hour. If he wants to be able to bake at least 230 cookies, how many hours will be have to spend in the kitchen? Interpret your solution in context.

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SLMConcept: Multi-step Equations

LEQs:4) If an equation has multiple steps, what

can I look for to help me simplify the equation before I try to solve?

5) How do we solve equations with variables on both sides?

Let’s remember the Distributive Property

43 x p 92

k15123

1

4843 x• Distributive and Solving

Check:

1652 r

Check:

• PROBLEM:A rectangular garden has a length of 6 feet and width of 4x+2 feet. What the area of the garden? (hint: Draw a picture)

What do you notice is different than you’ve seen before?

33435 xx

Check:

POD 1/16Solve. Check your answer!!1. 2.

3.

20)3(5 x xx 231130

582

x

15867 t

Check:

• If an equation has multiple steps, what can I look for to help me simplify the equation before I try to solve?

_______________________________________________________________________________________________________________

Answer LEQ

342)13(2 xx

Check:

83)3(5 x

Check:

• 3. A rectangular garden has dimensions, in feet, as show in the figure.

• Write an expression for the area of the rectangular garden.

• b. Find the area of the rectangular garden, in square feet, if x=3.

• c. Find the value of x if the area of the rectangular garden is 160 square feet.

• Susie and her two friends are trying to pool together their money to buy the new Dance Dance Revolution game. They all plan on babysitting to earn their money. Each girl decides that they will charge the same amount for their hourly rate. Susie already has $12 in her piggy bank and babysits for 5 hours. Glenda was asked to work for 8 hours, but unfortunately has nothing to contribute from her piggy bank. Relinda has $20 to contribute to the pool of money and worked 3 hours. The game costs $112.

• Write the equation to represent the situation showing each girl’s contribution to the purchase.

• Equation:_______________________________________

• Solve to find the hourly rate for babysitting.

Exit Ticket #1

Practice Page

• 1. 2. xx )13(217 64)129(355 xx

• 3. You earn $9 per hour. On major holidays, such as Thanksgiving, you earn twice as much per hour. You earned a total of $405 for the week including Thanksgiving. Write and solve an equation to find how many hours you worked on Thanksgiving if you worked 35 hours during the rest of the week.

Warm- UP: Happy Friday!1/17/14

The perimeter of right triangle ABC is 132. Find the length of the hypotenuse.

Quiz-Quiz Trade!• Partner A asks/shows partner B the question.• Partner B answers the question• Partner A responds with “You’re so SMART!!”

or “Can I help, you seem to be confused”• Switch Roles.• After both partners have been quizzed, trade

cards. • Put your hand up to find a new partner!!!

POD 10/17Determine the value of n if the perimeter of the

following figure is 86 units. (Figure not drawn to scale)

n + 6

5n – 3

45

n

12n

Photo BookBook Size Base Price

(first 20 pages included)Cost for Each additional Page

7-in by 9-in $20 $1.008-in by 11-in $25 $1.00

12-in by 12-in $45 $1.50

Write an equation between cost, y, in dollars and the number of pages, x, for each book size.

7-in by 9-in8-in by 11-in

12-in by 12-in

2. What is the cost a 12-in by 12-in book with 28 pages?

3. How many pages are in an 8-in by 11-in book that costs $49?

Book Size Base Price(first 20 pages included)

Cost for Each additional Page

7-in by 9-in $20 $1.008-in by 11-in $25 $1.00

12-in by 12-in $45 $1.50

TYPO- FIX

ADD TO NOTES

• Using a Balance to help us Solve Equations!• *Remember: = 1 positive variable

= 1 positive constant

= 1 negative variable = 1 negative constant

G

R

On your balances…• Show the equation 5213 xx

Solve Mathematically:

On your balances…• Show the equation 18587 xx

Solve Mathematically:

On your balances…• Show the equation 148112 bb

Solve Mathematically:

If you’re ready, try without…• Show the equation

25249 yySolve Mathematically:

If you’re ready, try without…• Show the equation

1659 aaSolve Mathematically:

If you’re ready, try without…• Show the equation

1935 nnSolve Mathematically:

If you’re ready, try without…• Show the equation

9272 xxSolve Mathematically:

POD 10/221. Write in exponential form using only positive exponents.

2. John is buying a jacket for $30. There is a 15% sales tax. How much will he pay for the jacket?

6

8

b

b

Variables on Both SidesSage and Scribe

Exit Ticket #2

A Party Surprise!

• While Nic and Emily were off to the mall, Aunt Heather was finalizing the details to rent a moon bounce for the family reunion picnic. She received cost estimates from two different companies that rent inflatable moon bounces.

Walkin’ on the Moon charges $55 per hour and a $100delivery charge to rent a moon bounce. Moo-na Lunacharges $65 per hour and a $75 delivery charge.

Write an expression to represent the cost of renting amoon bounce from Walkin’ on the Moon and Moo-na Luna.

Walkin’ on the Moon:_____________________

Moo-na Luna: ______________________

Will the cost ever be the same?• Complete the table to find the total cost for renting a

moon bounce from the two different companies. Will they ever cost the same amount of money?

Moon Bounce Rental time(in hours)

Walkin’ on the Moon total cost (in $)

Moo-na Luna total cost (in $)

1

1.5

2

2.5

3

Write an equation…• Write an equation that represents the cost of

the two companies being equal.

HOMEWORK: Solving with variables on both sides.

• 1. 6543 yy

• 2.

• 3. nn 12622

28.48.17.06.5 tt

4. Noelle needs to have her computer fixed. One company charges a $25 estimation fee plus $45 per hour. Another company charges a $10 estimation fee plus $60 per hour. Find the number of hours for which the two costs would be the same.

POD 12/6How many solutions does each equation have?

1. 2. 3. xx 3885 xxx 924)62(2412 xx

At the Mall…Nic and Emily arrive at the arcade and head to theirfavorite games. Nic plays Dinosaur Tag, which costs $0.75 agame and Emily plays Comet Avoidance, which costs $0.50a game.

• Nic has $15 to spend. Write an equation to determine how much money Nic will have after play Dinosaur Tag.

• How much money does Nic have after playing 4 games?• How about after 6?

At the Mall cont’d:Emily have $13 to spend. Write an equation todetermine how much money Emily will have afterplay Comet Avoidance.

Use your equation to determine how much money Emily has left after 4 games? After 6?

When?• After how many games played will Nic and

Emily have the same amount of money? Write an equation and solve.

• Explain your solution in terms of the problem.

Practice with Word Problems• 1. Travis and Bill both work at Target. One week they

were both paid the same amount. Travis worked 18 hours and Bill worked 26 hours. Travis had received a $50 bonus for good attendance. How much do Travis and Bill make per hour?

• a. Hourly Wage: ________________

• b. What was each of their paychecks? Travis: _______________ Bill: ______________

Blast from the Past!

# 3. Change to

When you’re done, please open to page 17 and work on #2.

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k

k

• 2. Pedro opened his account with $710 and withdrew $35 per week. Maria opened her account with $570 and withdrew $25 weekly. In how many weeks will their accounts be equal?

• 3. The Magic Carpet charges $90 for installation and $9 per square yard of carpeting. The Carpeteria’s installation price is $50 but the store charges $13 for each square yard. For what number of square yards of carpeting will the cost, including installation, be the same for both stores?

• Which store is cheaper to buy carpet from to carpet a room that is 48 square yards?

SKIP!!

• 4. Prestige Car Rentals charges $44 per day plus 6¢ per mile to rent a mid-sized vehicle. Gateway Auto charges $35 per day plus 9¢ per mile for the same car. For what number of miles will both companies charge the same price?

• a. If you need to travel from Delaware to San Francisco California, 2,891 miles, which company would be cheaper?

• 5. Nilda has $250 in her savings account. She plans to save $15 per week from her salary. Iona has only $200 in her account but can save $20 a week from her paycheck. How many weeks will it take before the amount in each savings account is the same?

• 6. A sales person in a stereo store is given a choice of two different compensation plans. One plan offers a weekly salary of $250 plus a commission of $25 for each stereo sold. The other plan offers no salary but pays $50 commission on each stereo sold. How many stereos must the sales person sell to make the same amount of money under both plans.

• a. If the sales person only averages 2 stereo sales a week, which option is more lucrative?

Who should deliver your Valentine’s Day gift?

• Phil looked up two different florists in order to get his Valentine a gift. For shipping “n” roses, Speedy Package Express would charge 3+2.25n dollars. The Fly By Night Express would charge 4+2n dollars. Solve the equation 3 + 2.25n = 4 + 2n. Explain what the solution tells you.

• Explain: ____________________________________________________________________________________________________________________________________

Semi-Formal Conundrum!

Stumps Party charges $1.10 per invitation as wellas a $20 design fee. Anderson’s Prom charges a$35 design fee and $0.90 per invitation. When dothe two companies cost the same?

Expression for Stumps:_____________Expression for Anderson:___________

Equation:____________________

If Mrs. Cap and Mrs. Haskell need invitations for 220students, what company should they order from to get the best deal?

3590.02010.1 xx

More variables on both sides practice!Be Careful!

1. 2210127 xx 2. 16314 xx 3. 1)15(2310 xx 4. 1)3(5)2(2 xx 5. 453273 xxx 6. xx 22)206(4

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Let’s Answer LEQ #5

• 5) How do we solve equations with variables on both sides?

Equation Sort!Cut each equation out.

Solve each equation.

Determine whether the equation has ONE, NONE or INFINITE solutions.

ONE NONE MANY

How Many Solutions?

One None Infinite Looks like: Solution:

Looks like: Solution:

Looks like: Solution:

Summarize: When you solve any equation, describe how you will know when there will be one, none, or infinite solutions. ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

POD 12/71. Write the equation.

2. Write the equation. Ben and Jerry have one ice cream store open. People love their ice cream so much that they’re tripling the amount of stores they open every year.

How many stores will they have open in five years?

x 2 3 4 5 6y 22 14 6 -2 -10

# 7 NEW TABLE

#12 The Washington Monument is 675 feet tall

0 1 2 3 42 4 8 16 32

POD 12/71. What is the length of the missing side.

40 cm

45 cm100 cm

? cm

Who should deliver your X-mas gifts?

• Bronco Electronics received bids from two shipping companies. For shipping “n” calculators, Speedy Package Express would charge 3+2.25n dollars. The Fly By Night Express would charge 4+2n dollars. Solve the equation 3+2.25n=4+2n. Explain what the solution tells you.

)2(435 xx

xx 19)89(

)6(265 xx

)23(5515 xx

)4(2)1(4 xx

Literal Equations• Let’s refresh our memory on solving two-

step equations. Solve the equations below and show all of your work.

Solve for x. Solve for x:

2x 5 12

mx n k

What’s the difference?

• What is different about the first equation and the second equation?

Literally…• The second equation, , is called a literal

equation. A literal equation is an equation with two or more variables. You are familiar with literal equations. You might know them better by the term “formula”. For example:

A1

2bh The area of a triangle

d rt Distance

V lwh Volume of a rectangular prism

Examples:• Algebra can be used to change the formula to

a more useful equivalent equation. The steps used in the process are very similar to those you used in solving linear equations. Let’s consider an example,

Examples: • Example 1: Solving a Literal Equation Involving

a Triangle

• Suppose that we know the area A and the base b of a triangle and want to find it’s height h.

• We are given:

A1

2bh

• Our job is to find an equivalent equation with h, the unknown, by itself on one side. First we can clear the fraction. Since ½ is multiplying by b and h, we can “undo” the operation by using the inverse and dividing by ½ . Dividing both sides of the equation by ½ is the same as multiplying by 2.

A1

2bh

• Finally, to isolate h on the right side of the equal sign, we must “undo” the operation of b. This means we need to divide both sides by b.

• Therefore, the equivalent equation, from the original formula for the area of a triangle is __________________.

bhA2

• Try one on your own!• Solve to find the h in the equation

for volume of a cone below. • Solve for h.

Solve for h.

V 1

3Bh

Practice:• 1. Solve for x:

• 2. Solve for r:

y mx b

C 2r

More Practice!!!

• 3. Solve for m:

• 4. Solve for E.

emc 2

I E

R

More Practice:• 5. Solve for T.

6. Solve for S.

V KT

P

DC Sn

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