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The strategy is: Analyze before the change occurred. Analyze after the change occurred.

Today we will explore the Essential Question, “What is the effect of changing a cost parameter in a given situation?". Prices and incomes are continually rising and falling. Often people are concerned with the effects of these changes on their finances.

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The strategy is: Analyze before the change occurred. Analyze after the change occurred.

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  1. Today we will explore the Essential Question, “What is the effect of changing a cost parameter in a given situation?" Prices and incomes are continually rising and falling. Often people are concerned with the effects of these changes on their finances. In a relation or function, an unknown quantity is called a variableand a known quantity is called a constant or a parameter. If the cost of x items is $5 per item, then the cost of all of the x items in dollars is 5x. In the expression 5x, the 5 is the constant or parameter and the x is the variable. In today's lesson we will solve problems that involve changing a cost parameter and determining its effect. • The strategy is: • Analyze before the change occurred. • Analyze after the change occurred. • Answer the question.

  2. Example 1: Vanessa spent $171 on gasoline last month when the average cost of gasoline was $1.90 per gallon. If she uses the same number of gallons of gasoline next month when the average cost of a gallon is $2.55, how much more money will she spend next month on gasoline? (1) Before (2) After Total cost: 90($2.55) = $229.50 Total cost: $171 Cost per Gallon: $2.55 Cost per gallon: $1.90 Gallons used: Gallons used: 90 $229.50 - $171 = $58.50 (3) Answer the question: The gasoline will cost Vanessa $58.50 more due to the price increase.

  3. Example 2: A telephone company charges a flat fee of $10.00 per month plus $0.25 per minute of usage. The bill for a customer one month was $22.25. Then the charge per minute of usage was changed to $0.20 per minute but the flat monthly fee did not change. If the same number of minutes is used the next month, what will the customer's savings be, in dollars, for the total bill? (1) Before (2) After $10 + $9.80 = $19.80 Total bill: Total bill: $22.25 Cost of minutes only: Cost of minutes only: 49(0.20) = $9.80 Cost per minute: $0.25 Cost per minute: $0.20 Minutes used: Minutes used: 49 (3) Answer the question: $22.25 - $19.80 = $2.45 The customer’s savings will be $2.45 due to the price decrease.

  4. Guided Practice Problems: 1. The cost to rent a bus for a class trip is $1080. Each student who goes on the trip has to pay an equal share of the cost. When the bus was ordered, 48 students had signed up to go on the trip but only 40 students actually went. Only those who rode on the bus had to pay. How much less would it have cost per student if all 48 who had signed up had ridden the bus? (1) Before (2) After Total bill: $1080 Total bill: $1080 Number of students: 48 40 Number of students: Cost per student: Cost per student: (3) Answer the question: $27 - $22.50 = $4.50 The savings per student would be $4.50.

  5. 2. The girls volleyball team needs to earn $2,000 to buy uniforms. Last year they raised $1,600 by selling popcorn in tins at $8 per tin. By how much would they have to increase the price of a tin of popcorn in order to achieve their goal if they can sell the same number of tins of popcorn this year? (1) Before (2) After Total to be raised: $2,000 Total raised: $1,600 Price of one tin: $8 Price of one tin: Number tins sold: 200 Number of tins sold: (3) Answer the question: $10 - $8 = $2 The price of one tin of popcorn would have to increase by $2.00.

  6. 3. Last year 4 local bands played at a spring break concert for a local school. Tickets were sold at $5 each and the money was used to pay each band $100 with the remaining $2725 going to the school's recreation fund. Next year 6 bands will play and be paid $100 each. If the tickets are still $5 each, how many tickets will have to be sold next year in order to raise the same amount of money as last year for the school's recreation fund? (1) Before (2) After Number of bands: 6 Number of bands: 4 Amount paid each band: $100 Amount paid each band: $100 Total to bands: 6($100) = $600 Total to bands: 4($100) = $400 Amount to school rec fund: $2725 Amount to school rec fund: $2725 Total amount made: Total needed: $600 + $2725 = $3325 $400 + $2725 = $3125 (3) Answer the question: tickets Next year 665 tickets will have to be sold.

  7. 4. A telephone company charges a flat fee of $20.00 per month plus $0.25 per minute of usage. The bill for a customer one month was $70.00. Then the charge per minute of usage was changed to $0.20 per minute but the flat monthly fee did not change. If the same number of minutes is used the next month, what will the customer's savings be, in dollars, for the total bill? (1) Before (2) After $20 + $40 = $60 Total bill: $70.00 Total bill: Cost of minutes only: Cost of minutes only: 200(0.20) = $40 Cost per minute: $0.25 Cost per minute: $0.20 Minutes used: Minutes used: 200 (3) Answer the question: $70 - $60 = $10 The customers savings will be $10 due to the price decrease.

  8. Independent Practice Problems: 1. A pizza delivery person is paid $5 per hour worked plus $3 for each pizza delivered. Last week he worked 35 hours and earned $265. This week he wants to earn $295. If he works the same number of hours this week, how many more pizzas must he deliver this week than he delivered last week? (2) After (1) Before Pay per hour: $5 Pay per hour: $5 Hours worked: 35 Hours worked: 35 Pay for hours worked: $5(35)=$175 Pay for hours worked: $5(35)=$175 Pay for pizzas: $295 - $175 = $120 Pay for pizzas: $265 - $175 = $90 Number of pizzas delivered: Number of pizzas delivered: (3) Answer the question: 40 – 30 = 10 more pizzas 2. A newspaper carrier earns $0.12 for each paper he delivers daily. He now delivers papers to 100 customers each day. If he increases the daily number of customers to120, how much more money would he earn each day? (1) Before (2) After Pay per paper: $0.12 Pay per paper: $0.12 Papers delivered: 120 Papers delivered: 100 Amount earned per day: Amount earned per day: $0.12(100)=$12 $0.12(120)=$14.40 (3) Answer the question: $14.40 - $12 = $2.40 more he will earn each day.

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