Unit 0

Solving Linear Equations

Hatter’s Café Menu

• Pancakes 2.25• Regular Eggs 1.05• Bacon 1.00• Ham 1.00• Toast .25• Juice 1.50• 2-2-2 Special 2.22

Ticket #1

P + H + JWhat did the customer order?

How do you know that?

How much is his order?

Pancakes, Ham and Juice

P for Pancakes, H for Ham and J for Juice

2.25 +1 +1.50 = $4.75

Here are some other orders. What do you think they mean?

Ticket #2S + J + B

Ticket #32B + E

Ticket #42H+E+3J

Special + Juice + Bacon

2 Bacon + 1 Egg

2Ham + Eggs + 3Juice

Some Large Orders: How much would it cost?

Ticket #52(E + T)

Ticket #6S + 2(B+J)

Ticket #73(S+J+P) + H

2 orders of (Egg and Toast)

1 Special + 2 orders of (Bacon and Juice)

3 orders of (Special+Juice+Pancackes) + 1Ham

Suppose you have $10 to spend. What are some possible orders you can make? Get as close to $10 as possible without going over.

“Messed up” orders

Ticket #8

(E+J) = $7.65What was ordered?How many were ordered?

How can you tell?

orders of (Egg and Juice)

3 orders of (Egg + Juice)

__ (1.05+1.50) = 7.65 Substitute into the equation what you know

__(2.55) = 7.65 Simplify

__= 3 Division Property of equality

“Messed up” orders

Ticket #9

S +3 = $2.97What was ordered? What was ordered? How much was it?

How can you tell?

Special + 3 orders of (___)

1 Special and 3(Toast for $0.25)

2.22 + 3(___) = 2.97 substitute into the equation

3(___) = 0.75 addition property of equality

(___) = 0.25 division property of equality

“Messed up” orders

Ticket #10

E +P = $6.45What was ordered?How many _____were ordered?

How can you tell?

__orders of (Eggs) + Pancakes

4 orders of (Egg) + 1 pancake

___(1.05) + 2.25 = 6.45 Substitute ___(1.05) = 4.20 Subtraction property of equality

___ = 4 division property of equality

“Messed up” ordersTicket #11

+ H + J = $3.55What was ordered?What was ordered? How many were

ordered?How can you tell?

__ + Ham + Juice

___ + 1 + 1.50 = 3.55 substitute

___ + 2.50 = 3.55 simplify

___ = 1.05 subtraction property of equality

1 Egg + 1 Ham + 1 Juice

Explain in your own way a fool proof way to solve messed up problems like these.

How could you solve these equation?

1) 2x + 4 = 24

2) 3(x+5) = 21

3) x = 18 64) 3x + 2(x+1) = 52

5) -2x = 10

x = 10

x = 108

x = 2

x = -5

x =10

More Examples with Explanations

• http://edweb.tusd.k12.az.us/sklein/Algebra/WEB%20powerpoints/3.1%20Solving%20equations%20with%20addition%20or%20subtraction.pps

• http://edweb.tusd.k12.az.us/sklein/Algebra/WEB%20powerpoints/3.2%20Solving%20equation%20with%20multiplication%20and%20division.pps

More Examples

• http://edweb.tusd.k12.az.us/sklein/Algebra/3.3%20Solving%20mulitple%20step%20equations.ppt

Solving Literal Equations

Solve a formula for one of its variable

Formula Vs. Function

• A function is an equations that relates two variables or quantities.

• A formula is an equation that relates two or more real-life quantities.

Using an Area Formula

In other words SOLVE FOR l

A=lwA = lw

1. Use the formula for the area of a rectangle:

2. Find a formula for l in terms of A and w.lwA

ww

lw

A

Now use the new formula to find the length of a rectangle with an area of 35ft2 and a width of 7 ft.

lw

A

lft

ft

7

35 2

lft 5

Solving the Formula for F

)32(9

5 FC

If it is 340C what is the temperature in F0?

5

9)32(

9

5

5

9 FC

)32(5

9 FC+32+32

FC 325

9

F32)34(5

9

Plug in 34 for c and solve

Using Another Formula: Simple Interest

Pt

t

Pt

I Pr

tI PrSolve for r.

What is my rate for an investment of $1500 if it made $54 in interest for one year?

rPt

I

Solving a function for x.

92 yx Rewrite the equations so that x is a function of y.

+ y + y

yx 92

22

yx2

1

2

9

rtD Solve the Distance formula for t

Solving a function for y…

43 yxRewrite the equation so that y is a function of x.

-3x -3x

xy 34

Practice…

bhA2

1 lwhV

Solve for b. Solve for h.

hrV 2Solve for h.

Practice… Solve for y

xxy

yx

yx

28)3(5

1032

52