Expressions vs. Equations

1. 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

2. Remember These? HUH?? Looks confusing – but it’s not! TC = VC*v ± FC OR TC = FC ± VC*v

3. The Cost Equation HUH?? Looks confusing – but it’s not! TC = VC*v ± FC OR TC = FC ± VC*v

4. Power Up: HW Out • Sit silently • Complete problems, show all work • HW: Test review, solving equations • (due Tomorrow, on lined paper)

5. Power Up: HW Out • Sit silently • Complete problems, show all work • HW: Writing Eq. from Word Problems • (due Tomorrow, on lined paper)

7. 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

8. 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

9. 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.

10. Total Cost/Amount Total Cost/Amount: the total cost or amount Examples: Total cost, total amount earned, total budget, total savings, etc.

11. 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

12. Example 1 A 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 Equation = 41 3n + 8 8 41

13. Solve 3n + 8 = 41 -8 -8 3n = 33 3 3 n = 11 letters 3(11) + 8 = 41 33 + 8 = 41

14. Practice 1a An 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 Equation 3x 3x + 6 = 18 6 18

15. Solve 3x + 6 = 18 -6 -6 3x = 12 3 3 x = 4 calculators 3(4) + 6 = 18 12 + 6 = 18

16. Practice 1b Equation 2t 2t + 20 = 42 20 42 To 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

17. Solve 2t + 20 = 42 -20 -20 2t = 22 2 2 t = 11 lines of text 2(11) + 20 = 42 22 + 20 = 42

18. Example 2 Equation = 32 4d 4d 12 + 12 32 Brianna 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

19. Solve 4d + 12 = 32 -12 -12 4d = 20 4 4 d = 5 dollars 4(5) + 12 = 32 20 + 12 = 32

20. Practice 2a Equation = 72 2m 2m 30 + 30 72 A 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

21. Solve 2m + 30 = 72 -30 -30 2m = 42 2 2 m = 21 minutes 2(21) + 30 = 72 42 + 30 = 72

22. WATCH OUT Sometimes the order of the fixed cost and the variable cost REALLY matters!

23. Practice 2a 25x Equation – = 150 200 25x 200 150 Ronnisha 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

24. Solve 200 – 25x = 150 -200 -200 -25x = -50 -25 -25 x = 2 shoes 200 – 25(2) = 150 200 – 50 = 150

25. Practice 3a 4d Equation – = 75 4d 25 25 75 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

26. Solve 4d – 25 = 75 +25 +25 4d = 100 4 4 d = 25 dollars 4(25) – 25= 75 100 – 25 = 75

27. Practice 3b 8h Equation + = 280 8h 40 40 280 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

28. Solve 8h + 40 = 280 -40 -40 8h = 240 8 8 h = 30 hours 8(30) + 40= 280 240 + 40 = 280

29. 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