Expressions vs. Equations

• 4x + 3 -2x and 3x + 31 = 32

• An expression is an operation with variables or numbers but no equal sign.– Example: 4x +5 or 4(x+5) ÷ 7

• An equation is an operation with variables or numbers with an equal sign.– Example: 4x +5 = 30 or 4(x+5) ÷ 7 = -20

Remember These?

TC = VC*v ± FC

OR

TC = FC ± VC*v

HUH??

Looks confusing – but it’s not!

The Cost Equation

TC = VC*v ± FC

OR

TC = FC ± VC*v

HUH??

Looks confusing – but it’s not!

Power Up: HW Out

• Sit silently

• Complete problems, show all work• HW: Test review, solving equations

– (due Tomorrow, on lined paper)

Power Up: HW Out

• Sit silently

• Complete problems, show all work• HW: Writing Eq. from Word Problems

– (due Tomorrow, on lined paper)

1) -1 x -6 = 6 11) -72 + 12 = -602) -18 / 2 = -9 12) 5 / 1 = 53) 36 - 4 = 32 13) -36 + -12 = -484) -12 x -5 = 60 14) -40 - 4 = -445) -6 + 1 = -5 15) -7 - -7 = 06) 9 / 3 = 3 16) -8 x 12 = -967) 6 x 5 = 30 17) -77 / -7 = 118) -22 - -2 = -20 18) -50 + -5 = -559) 72 + 6 = 78 19) -18 - 9 = -27

10) 1 x 2 = 2 20) 45 / 5 = 9

Writing Equations from Word Problems

• All about solving problems

• Need for: budgeting, running a business, making decisions about using materials, saving money, or spending time

Constant/ Starting amount

Something you pay or do one time, the amount where you start

Examples: Flat fees, starting amounts, upfront costs, down payments, current savings, $_ off coupons, how much money you have

Rate of Change the amount or cost it increases or decreases by,

depending on the variable [how much you buy, how many hours you work, etc.]

***multiply by the variable***Examples: Price per item, miles per hour, hourly

wage, percent (%) of something, tax, tip, commission, etc.

Total Cost/AmountTotal Cost/Amount: the total cost or amount

Examples: Total cost, total amount earned, total budget, total savings, etc.

Definitions

Fixed Cost/Amount: a cost or amount that doesn’t change no matter what

Variable Cost/Amount: a cost or amount that changes depending on what you do to the variable

Total Cost/Amount: the total amount or final result

Example 1A blank trophy costs $8. Each letter (n) engraved on the

trophy costs $3. The cost of the trophy with the letters was $41. Write an equation that you would use to solve for the cost of each letter (n) on the trophy.

Variable Cost

Fixed Cost

Total Cost

3n

8

41

Equation

= 413n 8+

Solve

3n + 8 = 41 -8 -8 3n = 33 3 3 n = 11 letters3(11) + 8 = 41 33 + 8 = 41

Practice 1aAn empty box weighs 6 ounces. Jena puts x calculators into

the box. Each calculator is 3 ounces. The weight of the box with the calculators inside is 18 ounces. Write an equation you could use to solve for the number x of calculators in the box.

Variable Cost

Fixed Cost

Total Cost

3x

6

18

Equation

= 183x 6+

Solve

3x + 6 = 18 -6 -6 3x = 12 3 3 x = 4 calculators3(4) + 6 = 18 12 + 6 = 18

Practice 1bTo place an ad on Facebook, there is a flat fee of $20

and an additional charge of $2 per line of text (t). If the cost of the ad was $42, how many lines of text (t) were in the ad?

Variable Cost

Fixed Cost

Total Cost

2t

20

42

Equation

= 422t 20+

Solve

2t + 20 = 42 -20 -20 2t = 22 2 2 t = 11 lines of text2(11) + 20 = 42 22 + 20 = 42

Example 2Brianna held a carwash to raise money for her

volleyball team. They washed 4 cars and received $12 in donations. The total amount they collected was $32. Write an equation to calculate the money (d) they earned for eafch car.

Variable Cost

Fixed Cost

Total Cost

4d

12

32

Equation

= 324d 12+

Solve

4d + 12 = 32 -12 -12 4d = 20 4 4 d = 5 dollars4(5) + 12 = 32 20 + 12 = 32

Practice 2aA telephone company charges a $30 one-time

connect fee and $2 a minute (m) for international calls. How many international minutes (m) were used if the first bill was for $72?

Variable Cost

Fixed Cost

Total Cost

2m

30

72

Equation

= 722m 30+

Solve

2m + 30 = 72 -30 -30 2m = 42 2 2 m = 21 minutes2(21) + 30 = 72 42 + 30 = 72

WATCH OUT

Sometimes the order of the fixed cost and the variable cost REALLY matters!

Practice 2aRonnisha has $200 saved in the bank. She wants to

buy shoes for $25 each. After buying x shoes, she has $150 left in the bank. Write an equation to model this situation.

Variable Cost

Fixed Cost

End Result

25x

200

150

Equation

= 150200 25x–

Solve

200 – 25x = 150 -200 -200 -25x = -50 -25 -25 x = 2 shoes200 – 25(2) = 150 200 – 50 = 150

Practice 3a Four friends went to dinner and ordered meals which

cost d dollars each, including tax and tip. They had a $25 off coupon and paid a total of $75. Write an equation to determine how much each meal cost.

Variable Cost

Fixed Cost

Total Cost

4d

25

75

Equation

= 754d 25–

Solve

4d – 25 = 75 +25 +25 4d = 100 4 4 d = 25 dollars4(25) – 25= 75 100 – 25 = 75

Practice 3b Kareem works for $8 an hour h and has already saved

$40. He is working towards buying an ipod that costs $280. Write an equation to express how many hours he needs to work before he can buy the ipod.

Variable Cost

Fixed Cost

Total Cost

8h

40

280

Equation

= 2808h 40+

Solve

8h + 40 = 280 -40 -408h = 240 8 8 h = 30 hours8(30) + 40= 280 240 + 40 = 280

New Activity

• In your groups you will get one set of cards and one card placemat.

• You will be given problems one by one to write the equation represented. To do this, place the cards in the right order on the placemat.

• Once you have done this, raise your hand and I will come check you off– Then fill out the worksheet for that problem

• Then you will get a new problem