Modeling Equations

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Misc. (Math Is Super Cool)

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Let y = 250x + 1000 represent the amount of money (in dollars) in your savings account from 1994 until 2009. Let x represent the number of years since 1994. What is the rate of change in the linear model? Estimate the amount of savings you will have in 2020.

$7,500.00

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Let y = 5.6x + 8.1 represent a company’s profit (in thousands of dollars) from 1995 to 2005.  Let x represent the number of years since 1995.  What is the rate of change of the linear model?  What is the y-intercept of the linear model?

Rate of Change = $5.6 thousand per yearY-intercept = $8.1 thousand

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Let y = 5.6x + 8.1 represent a company’s profit (in thousands of dollars) from 1995 to 2005. 

Let x represent the number of years since 1995.  What does the rate of change of the linear model represent in real life? 

What does the y-intercept of the linear model represent in real life?

The rate of change represents the increase in profit per year. The y-intercept represents the company’s profit in 1995.

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Let y = 5.6x + 8.1 represent a company’s profit (in thousands of dollars) from 1995 to 2005.  Let x represent the number of years since 1995.  Predict the company’s profit in 2009.

$86.5 thousand

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Let y = 5.6x + 8.1 represent a company’s profit (in thousands of dollars) from 1995 to 2005.  Let x represent the number of years since 1995.  Predict the company’s profit in 2050. 

$316 thousand

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Let y = 0.3x + 36 represent a chemist’s salary (in thousands of dollars) from 1988 to 1998  Let x

represent the number of years since 1985.  What is the y-intercept in the linear model? What is the Slope

of the linear model?

Y-intercept = 36 Slope = 0.3

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Let y = 0.3x + 36 represent a chemist’s salary (in thousands of dollars) from 1988 to 1998.  Let x represent the number of

years since 1988.  Estimate a chemist’s salary in 2009.

$42.3 thousand

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Let y = 0.3x + 36 represent a chemist’s salary (in thousands of dollars) from 1988 to 1998.  Let x represent the number of years since 1988.  Estimate a chemist’s salary in 2020.

$45.6 thousand

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You take up underwater basket weaving as a summer job.  Large baskets sell for $15.  Small baskets sell for $8.  You want to earn $250 for a new ipod.  Write an equation to represent the different numbers of large and small baskets you could sell.  Let x represent the number of large baskets.  Let y represent the number of small baskets.

15x + 8y = 250

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Bought a lawnmower this past summer for $250.  You are saving money to buy a new car.  For each lawn you mow, you charge $10.  Write an equation to represent your profit during the summer, y, in terms of the number of lawns you mow, x. 

y = 10x + -250

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You have a lemonade stand in your driveway.  It costs $0.10 for a cup of lemonade and $0.25 for a rice-crispy treat.  You want to earn $10 to pay your brother back for doing your chores last week.  Write an equation to model the situation where x represents glasses of lemonaide and y represents rice-crispy treats.

.1x + .25y = 10

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You are planning your schools fall sports banquet.  5 pans of lasagna costs a total of $70.  10 pans of lasagna costs a total of $120.  Write an equation to represent the cost of lasagna in terms of the number of pans your order.

y = 10x + 20

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You have $15 to buy basil and strawberry seedlings for your garden.  The basil seedlings cost $3 and the strawberry seedlings cost $6.  Write an equation to represent the

different amounts of basil and strawberry seedlings you could buy where x stands for the number of basil seedlings

you buy and y stands for the number of strawberry seedlings you buy.

3x + 6y = 15

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You are ordering doughnuts for the after school program at the grade school you help out at.  You can get 5 trays of doughnuts for $30.  You can get 7 trays of doughnuts for $40.  Write an equation to represent the cost of the order, y, in terms of the number of trays you purchase, x.

y = 5x + 5

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Giancarlo’s Pizzeria charges $18 for an 18 inch large pizza plus an additional $0.80 per topping you choose to add.   Write an equation to represent the cost of a large pizza in terms of the number of toppings you add 

y = .8x + 18

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Boat rentals at Devil’s Lake cost $15 for the first hour and then $10 for each additional hour after the first.  Write an equation to model this situation where y represents the cost (in dollars) and x represents the number of hours after the first hour. 

y = 10x + 15

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A campsite in Wisconsin Dells costs $50 for the first day and then $20 for each additional day after the first.  Write an equation to model this situation where y represents the cost (in dollars) and x represents the number of days after the first day. 

Y = 20x + 50

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You go a hike.  You begin at an elevation of 20 feet above sea level.  After hiking 20miles, you are 400 feet above sea level.  Write an equation to represent your elevation (measured in feet above sea level) in terms of miles you have hiked.

y = 19x + 20

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You are training for an iron man competition and so you join a gym.  There is a registration fee (paid one time) and then a monthly rate.  A 6 month gym membership costs a total $180 a 12 month gym membership costs a total of

$300.  Write an equation to model the cost of a gym membership in terms on the number of months you are a

member.

y = 20x + 60

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You want to rent a row boat for your trip.  The fee is $10 plus an additional $5 an hour.  Write an equation to model the situation.  Then fill in the table. 

X (Hours)  1  3  5  7Y (cost)  

y = 5x + 10

15, 25, 35, 45

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You deposit $200 into the bank on your 10th birthday plus an additional $100 each year.  Write an equation to

represent the amount of money in the bank in terms of the number of years it’s been since your 10th birthday.

y = 100x + 200

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A cell phone company charges $7 a month for unlimited text messaging plus $0.03 each minute you talk.  Write an equation to represent the cost of someone’s phone bill in terms of the number of minutes they talk.

y = .03x + 7

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Three days at doggie daycare costs $110. Five days at doggie daycare costs $170. 

Write an equation to represent the cost at the daycare in terms of the number of days the dog is there.

y = 30x + 20

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The temperature at 12:00 pm is 40 degrees and it is decreasing at an average rate of 3 degrees per hour until 12:00 midnight.  Write an equation to represent the temperature in terms of time (hours since noon).

y = -3x + 40

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You can purchase general ride tickets at the fair for $2 a ticket.  You can purchase “kiddie ride” tickets at the fair for $1 a ticket.  Write an equation to represent the

number of tickets you can buy with $20. 

2x + y = 20

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