The manager of a restaurant found that the cost to produce 100 cups of coffee is $63.00, while the cost to produce 350 cups is $188.00. Assume the relationshipbetween the cost y to produce x cups of coffee is linear.a. Write a linear equation that expresses the cost, y, in terms of the number of cups of coffee, x.b. How many cups of coffee are produced if the cost of production is $253.00?a. y=(Use integers or decimals for any numbers in the expression.)b. The total number of cups produced for a cost of $253.00 is cups. (Simplify your answer.)

Answered: The manager of a restaurant found that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3) A vendor of hot dogs at school ball games profits $100 on the sale of 300 hot dogs and $130 on the sale of 360 hot dogs. Assume a linear relationship between profit and the quantity x of hot dogs. a. Find the equation that illustrates the relationship between the profits earned and the number of hot dogs sold. b. What does the slope of the line tell us? С. How many hot dogs would need to be sold in order to break even?
The taxes for a primary residence can be described by a linear relationship. Find the equation for the relationship if the taxes for a home valued at $200,000 are $2400, and the taxes are $3150 when the home is valued at $250,000. Let y be the taxes and x the value of the home. Write the equation in slope-intercept form.
An engineer determined that the weight of a car and gas mileage have a linear relationship. A car that weighs 3500 pounds has a gas mileage of 20 miles per gallon. Another car that weighs 2500 pounds has a gas mileage of 29 miles per gallon. Let x be the weight of the car and y be the gas mileage of the car in miles per gallon. Use the point-slope formula to write a linear equation.
You decide to purchase a brand new boat for $20,000. You sell it 7 years later for its worth of $7500. Assuming the boat's value depreciates linearly, how much was it worth 4.5 years after you bought it? It is worth S (Round answer to nearest dollar.)
In 1960, there were 242,900 immigrants admitted to a country. In 2005, the number was 1,011,507. a. Assuming that the change in immigration is linear, write an equation expressing the number of immigrants, y, in terms of t, the number of years after 1900. b. Use your result in part a to predict the number of immigrants admitted to the country in 2013. c. Considering the value of the y-intercept in your answer to part a, discuss the validity of using this equation to model the number of immigrants throughout the entire 20th century. a. A linear equation for the number of immigrants is y=. (Type your answer in slope-intercept form. Type an expression using t as the variable. Use integers or decimals for any numbers in the equation. Type an integer or decimal rounded to two decimal places as needed.)
For an Uber driver (taxi driver) the following linear equation describes the relationship between the number of miles driven x, and the total cost y (in dollars).y = 1.99x + 2.75According to this equation,a. What is the cost of driving around town for 25 miles? b. If the total cost was $80.36, then how many miles did a passenger travel?

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