Expressions vs. Equations 4x x 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)

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/Amount Total 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 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 8 41 Equation = 41 3n8+

Solve 3n + 8 = n = n = 11 letters 3(11) + 8 = = 41

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 3x 6 18 Equation = 18 3x 6+

Solve 3x + 6 = x = x = 4 calculators 3(4) + 6 = = 18

Practice 1b 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 2t Equation = 42 2t 20+

Solve 2t + 20 = t = t = 11 lines of text 2(11) + 20 = = 42

Example 2 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 4d Equation = 32 4d12 +

Solve 4d + 12 = d = d = 5 dollars 4(5) + 12 = = 32

Practice 2a 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 2m Equation = 72 2m30 +

Solve 2m + 30 = m = m = 21 minutes 2(21) + 30 = = 72

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

Practice 2a 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 25x Equation = x –

Solve 200 – 25x = x = x = 2 shoes 200 – 25(2) = – 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 Equation = 75 4d25 –

Solve 4d – 25 = d = d = 25 dollars 4(25) – 25= – 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 Equation = 280 8h40 +

Solve 8h + 40 = h = h = 30 hours 8(30) + 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