Exer. 122: Solve the system

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

Exer. 122: Solve the system.

The price of admission to a high school play was $3.00 for students and $4.50 for nonstudents. If 450 tickets were sold for a total of $1555.50, how many of each kind were purchased?

An airline that flies from Los Angeles to Albuquerque with a stopover in Phoenix charges a fare of $90 to Phoenix and a fare of $120 from Los Angeles to Albuquerque. A total of 185 passengers boarded the plane in Los Angeles, and fares totaled $21,000. How many passengers got off the plane in Phoenix?

A crayon 8 centimeters in length and 1 centimeter in diameter will be made from 5 of colored wax. The crayon is to have the shape of a cylinder surmounted by a small conical tip (see the figure). Find the length x of the cylinder and the height y of the cone.

A man rows a boat 500 feet upstream against a constant current in 10 minutes. He then rows 300 feet downstream (with the same current) in 5 minutes. Find the speed of the current and the equivalent rate at which he can row in still water.

A large table for a conference room is to be constructed in the shape of a rectangle with two semicircles at the ends (see the figure). The table is to havea perimeter of 40 feet, and the area of the rectangular portion is to be twice the sum of the areas of the two ends. Find the length l and the width w of the rectangular portion.

A woman has $19,000 to invest in two funds that pay simple interest at the rates of 4% and 6% per year. Interest on the 4% fund is tax-exempt; however, income tax must be paid on interest on the 6% fund. Being in a high tax bracket, the woman does not wish to invest the entire sum in the 6% account. Is there a way of investing the money so that she will receive $1000 in interest at the end of one year?

A bobcat population is classified by age into kittens (less than 1 year old) and adults (at least 1 year old). All adult females, including those born the prior year, have a litter each June, with an average litter size of 3 kittens. The springtime population of bobcats in a certain area is estimated to be 6000, and the male-female ratio is one. Estimate the number of adults and kittens in the population

A 300-gallon water storage tank is filled by a single inlet pipe, and two identical outlet pipes can be used to supply water to the surrounding fields (see the figure). It takes 5 hours to fill an empty tank when both outlet pipes are open. When one outlet pipe is closed, it takes 3 hours to fill the tank. Find the flow rates (in gallons per hour) in and out of the pipes.

A silversmith has two alloys, one containing 35% silver and the other 60% silver. How much of each should be melted and combined to obtain 100 grams of an alloy containing 50% silver?

A merchant wishes to mix peanuts costing $3 per pound with cashews costing $8 per pound to obtain 60 pounds of a mixture costing $5 per pound. How many pounds of each variety should be mixed?

An airplane, flying with a tail wind, travels 1200 miles in 2 hours. The return trip, against the wind, takes hours. Find the cruising speed of the plane and the speed of the wind (assume that both rates are constant).

A stationery company sells two types of notepads to college bookstores, the first wholesaling for 50 and the second for 70. The company receives an order for 500 notepads, together with a check for $286. If the order fails to specify the number of each type, how should the company fill the order?

As a ball rolls down an inclined plane, its velocity (in ) at time t (in seconds) is given by for initial velocity and acceleration a (in ). If and , find and a.

If an object is projected vertically upward from an altitude of feet with an initial velocity of , then its distance above the ground after t seconds is If and , what are and ?

A small furniture company manufactures sofas and recliners. Each sofa requires 8 hours of labor and $180 in materials, while a recliner can be built for $105 in 6 hours. The company has 340 hours of labor available each week and can afford to buy $6750 worth of materials. How many recliners and sofas can be produced if all labor hours and all materials must be used?

A rancher is preparing an oat-cornmeal mixture for livestock. Each ounce of oats provides 4 grams of protein and 18 grams of carbohydrates, and an ounce of cornmeal provides 3 grams of protein and 24 grams of carbohydrates. How many ounces of each can be used to meet the nutritional goals of 200 grams of protein and 1320 grams of carbohydrates per feeding?

number of hours spent on each of the projects is shown in the following table. They would prefer to call the matter even, but because of tax laws, they must charge for all work performed. They agree to select hourly wage rates so that the bill on each project will match the income that each person would ordinarily receive for a comparable job. (a) If x and y denote the hourly wages of the plumber and electrician, respectively, show that and Describe the solutions to this system. (b) If the plumber ordinarily makes $35 per hour, what should the electrician charge?

Find equations for the altitudes of the triangle with vertices , , and , and find the point at which the altitudes intersect.

As a result of urbanization, the temperatures in Paris have increased. In 1891 the average daily minimum and maximum temperatures were 5.8C and 15.1C, respectively. Between 1891 and 1968, these average temperatures rose and , respectively. Assuming the increases were linear, find the year when the difference between the minimum and maximum temperatures was 9C, and determine the corresponding average maximum temperature.

A telephone company charges customers a certain amount for the first minute of a long distance call and another amount for each additional minute. A customer makes two calls to the same city a 36-minute call for $2.93 and a 13-minute call for $1.09. (a) Determine the cost for the first minute and the cost for each additional minute. (b) If there is a federal tax rate of 3.2% and a state tax rate of 7.2% on all long distance calls, find, to the nearest minute, the longest call to the same city whose cost will not exceed $5.00.

An avid tennis watcher wants to record 6 hours of a major tournament on a single tape. Her tape can hold 5 hours and 20 minutes at the LP speed and 8 hours at the slower SLP speed. The LP speed produces a better quality picture, so she wishes to maximize the time recorded at the LP speed. Find the amount of time to be recorded at each speed.

Suppose consumers will buy 1,000,000 T-shirts if the selling price is $15, but for each $1 increase in price, they will buy 100,000 fewer T-shirts. Moreover, suppose vendors will order 2,000,000 T-shirts if the selling price is $20, and for every $1 increase in price, they will order an additional 150,000. (a) Express the number Q of T-shirts consumers will buy if the selling price is p dollars. (b) Express the number K of T-shirts vendors will order if the selling price is p dollars. (c) Determine the market pricethat is, the price when

Exer. 4548: Solve the system for a and b. (Hint: Treat terms such as , cos x, and sin x as constant coefficients.)

Exer. 4548: Solve the system for a and b. (Hint: Treat terms such as , cos x, and sin x as constant coefficients.)

Exer. 4548: Solve the system for a and b. (Hint: Treat terms such as , cos x, and sin x as constant coefficients.)

Exer. 4548: Solve the system for a and b. (Hint: Treat terms such as , cos x, and sin x as constant coefficients.)