0.1 Linear equations: homework

In the U. S. the number of people infected with the HIV virus in 1985 was 1,000, and in 1995 that number became 350,000. If the increase in the number is linear, write an equation that will give the number of people infected in any year. If this trend continues, what will the number be in 2010? (Hint: See previous problem.)

In 1975, an average house in San Jose cost $45,000 and the same house in 1995 costs $195,000. Write an equation that will give the price of a house in any year, and use this equation to predict the price of a similar house in the year 2010.

An average math text book cost $25 in 1980, and $60 in 1995. Write an equation that will give the price of a math book in any given year, and use this equation to predict the price of the book in 2010.

Solve for $x$ and $y$ .
$y=\mathrm{3x}+4$
$y=\mathrm{5x}-2$

Solve for $x$ and $y$ .
$\mathrm{2x}-\mathrm{3y}=4$
$\mathrm{3x}-\mathrm{4y}=5$

The supply curve for a product is $y=\text{2000}x+\text{13000}$ , and the demand curve is $y=-\text{1000}x+\text{28000}$ , where $x$ represents the price and y the number of items. At what price will the supply equal demand, and how many items will be produced at that price?

The supply curve for a product is $y=\text{300}x+\text{9000}$ , and the demand curve is $y=-\text{100}x+\text{14000}$ , where $x$ represents the price and $y$ the number of items. At what price will the supply equal demand, and how many items will be produced at that price?

A demand curve for a commodity is the number of items the consumer will buy at different prices. It has been determined that at a price of $2 a store can sell 2400 of a particular type of toy dolls, and for a price of $8 the store can sell 600 such dolls. If $x$ represents the price of dolls and $y$ the number of items sold, write an equation for the demand curve.

A supply curve for a commodity is the number of items of the product that can be made available at different prices. A manufacturer of toy dolls can supply 2000 dolls if the dolls are sold for $8 each, but he can supply only 800 dolls if the dolls are sold for $2 each. If $x$ represents the price of dolls and $y$ the number of items, write an equation for the supply curve.

The equilibrium price is the price where the supply equals the demand. From the demand and supply curves obtained in the previous two problems, find the equilibrium price, and determine the number of items that can be sold at that price.

A car rental company offers two plans. Plan I charges $10 a day and 10 cents a mile, while Plan II charges 14 cents a mile, but no flat fee. If you were to drive 300 miles in a day, which plan is better? For what mileage are both rates equal?

A break-even point is the intersection of the cost function and the revenue function, that is, where the total cost equals revenue. Mrs. Jones Cookies Store's revenue and cost in dollars for $x$ number of cookies is given by $R=\text{.}\text{80}x$ and $C=\text{.}\text{05}x+\text{3000}$ . Find the number of cookies that must be sold so that the revenue and cost are the same.

A company's revenue and cost in dollars are given by $R=\text{225}x$ and $C=\text{75}x+\text{6000}$ , where $x$ is the number of items. Find the number of items that must be produced to break-even.