The perimeter of a tennis court is 228 feet. After a round

Fill in each blank so that the resulting statement is true. Suppose that x represents the cost of one apple and y represents the cost of one banana. The cost of five apples and six bananas is represented by ______________.

Fill in each blank so that the resulting statement is true. Suppose that x represents the length of a rectangular lot, in feet, and y represents its width, in feet. The cost of fencing the entire lot at 10 per foot for the length and 15 per foot for the width is represented by ______________.

Fill in each blank so that the resulting statement is true. A solar heating system costs 25,600 to install and has operating costs of 225 per year. The total cost for the solar system after x years is represented by ______________.

Fill in each blank so that the resulting statement is true. The combined yearly interest for x dollars invested at 4 and y dollars invested at 5 is represented by ______________.

Fill in each blank so that the resulting statement is true. The total amount of acid in x milliliters of a 7 acid solution and y milliliters of a 15 acid solution is represented by ______________.

Fill in each blank so that the resulting statement is true. If x represents the average rate of a plane in still air and y represents the average rate of the wind, the planes rate with the wind is represented by ______________ and the planes rate against the wind is represented by ______________.

Fill in each blank so that the resulting statement is true. If x y represents a motorboats rate with the current, in miles per hour, its distance after 4 hours is represented by ______________.

In Exercises 14, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 17. If one number is subtracted from the other, their difference is 3. Find the numbers.

In Exercises 14, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 5. If one number is subtracted from the other, their difference is 13. Find the numbers.

In Exercises 14, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. Three times a first number decreased by a second number is 1. The first number increased by twice the second number is 23. Find the numbers.

In Exercises 14, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of three times a first number and twice a second number is 43. If the second number is subtracted from twice the first number, the result is 4. Find the numbers.

The bar graph shows the average time per day that Americans devote to sprucing up. Exercises 56 are based on the graph. Each day, the sum of the average times spent on grooming for 20- to 24-year-old women and men is 86 minutes. The difference between grooming times for 20- to 24-year-old women and men is 12 minutes. How many minutes per day do 20- to 24-year-old women and men spend on grooming?

The bar graph shows the average time per day that Americans devote to sprucing up. Exercises 56 are based on the graph. Each day, the sum of the average times spent on grooming for 15- to 19-year-old women and men is 96 minutes. The difference between grooming times for 15- to 19-year-old women and men is 22 minutes. How many minutes per day do 15- to 19-year-old women and men spend on grooming?

Looking for Mr. Goodbar? Its probably not a good idea if you want to look like Mr. Universe or Kate Winslet. The graph shows the four candy bars with the highest fat content, representing grams of fat and calories in each bar. Exercises 710 are based on the graph. One Mr. Goodbar and two Mounds bars contain 780 calories. Two Mr. Goodbars and one Mounds bar contain 786 calories. Find the caloric content of each candy bar. (In Exercises 810 refer to the bar graph to visualize that your solution is reasonable).

(In Exercises 810 refer to the bar graph to visualize that your solution is reasonable). One Snickers bar and two Reeses Peanut Butter Cups contain 737 calories. Two Snickers bars and one Reeses Peanut Butter Cup contain 778 calories. Find the caloric content of each candy bar.

(In Exercises 810 refer to the bar graph to visualize that your solution is reasonable). A collection of Halloween candy contains a total of five Mr. Goodbars and Mounds bars. Chew on this: The grams of fat in these candy bars exceed the daily maximum desirable fat intake of 70 grams by 7.1 grams. How many bars of each kind of candy are contained in the Halloween collection?

(In Exercises 810 refer to the bar graph to visualize that your solution is reasonable). A collection of Halloween candy contains a total of 12 Snickers bars and Reeses Peanut Butter Cups. Chew on this: The grams of fat in these candy bars exceed twice the daily maximum desirable fat intake of 70 grams by 26.5 grams. How many bars of each kind of candy are contained in the Halloween collection?

In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and three shirts cost 42, while three sweaters and two shirts cost 56, find the price of one sweater and the price of one shirt.

A restaurant purchased eight tablecloths and five napkins for $106. A week later, a tablecloth and six napkins were bought for 24. Find the cost of one tablecloth and the cost of one napkin, assuming the same prices for both purchases.

The perimeter of a badminton court is 128 feet. After a game of badminton, a players coach estimates that the athlete has run a total of 444 feet, which is equivalent to six times the courts length plus nine times its width. What are the dimensions of a standard badminton court?

The perimeter of a tennis court is 228 feet. After a round of tennis, a players coach estimates that the athlete has run a total of 690 feet, which is equivalent to 7 times the courts length plus four times its width. What are the dimensions of a standard tennis court?

A rectangular lot whose perimeter is 320 feet is fenced along three sides. An expensive fencing along the lots length costs 16 per foot. An inexpensive fencing along the two side widths costs only 5 per foot. The total cost of the fencing along the three sides comes to 2140. What are the lots dimensions?

A rectangular lot whose perimeter is 1600 feet is fenced along three sides. An expensive fencing along the lots length costs 20 per foot. An inexpensive fencing along the two side widths costs only 5 per foot. The total cost of the fencing along the three sides comes to 13,000. What are the lots dimensions?

You are choosing between two telephone plans. Plan A has a monthly fee of 20 with a charge of 0.05 per minute for all calls. Plan B has a monthly fee of $5 with a charge of 0.10 per minute for all calls. a. For how many minutes of calls will the costs for the two plans be the same? What will be the cost for each plan? b. If you make approximately 10 calls per month, each averaging 20 minutes, which plan should you select? Explain your answer.

You are choosing between two telephone plans. Plan A has a monthly fee of $15 with a charge of $0.08 per minute for all calls. Plan B has a monthly fee of $3 with a charge of $0.12 per minute for all calls. a. For how many minutes of calls will the costs for the two plans be the same? What will be the cost for each plan? b. If you make approximately 15 calls per month, each averaging 30 minutes, which plan should you select? Explain your answer.

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $100 and you pay 80% of the manufacturers recommended list price. Plan B offers an annual membership fee of $40 and you pay 90% of the manufacturers recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $300 and you pay 70% of the manufacturers recommended list price. Plan B offers an annual membership fee of $40 and you pay 90% of the manufacturers recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

A community center sells a total of 301 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $487 in ticket sales. Find the number of each type of ticket sold.

On a special day, tickets for a minor league baseball game cost $5 for adults and $1 for students. The attendance that day was 1281 and $3425 was collected. Find the number of each type of ticket sold.

At the 1987 annual meeting of the National Council of Teachers of Mathematics, the system below was found on a menu card at a restaurant in California. Find the cost of each item in column A and the cost of each item in column B.

The perimeter of the rectangle is 34 inches. The perimeter of the triangle is 30 inches. a. Find the values of x and y. b. Find the area of the rectangle and the area of the triangle. y 1 x y x y

Nutritional information for macaroni and broccoli is given in the table at the top of the next column. How many servings of each would it take to get exactly 14 grams of protein and 48 grams of carbohydrates? Macaroni Broccoli Protein (grams/serving) 3 2 Carbohydrates (grams/serving) 16 4

The calorie-nutrient information for an apple and an avocado is given in the table. How many of each should be eaten to get exactly 1000 calories and 100 grams of carbohydrates? One Apple One Avocado Calories 100 350 Carbohydrates (grams) 24 14

In Exercises 2728, an isosceles triangle in which angles B and C have the same measure is shown. Find the measure of each angle whose degree measure is represented with variables. x + 8y 1 3y + 4 7x + 5 B C A

In Exercises 2728, an isosceles triangle in which angles B and C have the same measure is shown. Find the measure of each angle whose degree measure is represented with variables. 4x + 2y 9y 2 10x + 10 A B C

Exercises 2934 involve dual investments You invested $7000 in two accounts paying 6% and 8% annual interest. If the total interest earned for the year was $520, how much was invested at each rate?

Exercises 2934 involve dual investments You invested $11,000 in stocks and bonds, paying 5% and 8% annual interest. If the total interest earned for the year was $730, how much was invested in stocks and how much was invested in bonds?

Exercises 2934 involve dual investments You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total of $900. This year, the first fund paid a 10% dividend and the second only 1%, and you received a total of $860. How much money did you invest in each fund?

Exercises 2934 involve dual investments You invested money in two funds. Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330. This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500. How much money did you invest in each fund?

Exercises 2934 involve dual investments Things did not go quite as planned. You invested $20,000, part of it in a stock with a 12% annual return. However, the rest of the money suffered a 5% loss. If the total annual income from both investments was $1890, how much was invested at each rate?

Exercises 2934 involve dual investments Things did not go quite as planned. You invested $30,000, part of it in a stock with a 14% annual return. However, the rest of the money suffered a 6% loss. If the total annual income from both investments was $200, how much was invested at each rate?

Exercises 3542 involve mixtures. A wine company needs to blend a California wine with a 5% alcohol content and a French wine with a 9% alcohol content to obtain 200 gallons of wine with a 7% alcohol content. How many gallons of each kind of wine must be used?

Exercises 3542 involve mixtures. A jeweler needs to mix an alloy with a 16% gold content and an alloy with a 28% gold content to obtain 32 ounces of a new alloy with a 25% gold content. How many ounces of each of the original alloys must be used?

Exercises 3542 involve mixtures. For thousands of years, gold has been considered one of Earths most precious metals. One hundred percent pure gold is 24-karat gold, which is too soft to be made into jewelry. In the United States, most gold jewelry is 14-karat gold, approximately 58% gold. If 18-karat gold is 75% gold and 12-karat gold is 50% gold, how much of each should be used to make a 14-karat gold bracelet weighing 300 grams?

Exercises 3542 involve mixtures. In the Peanuts cartoon shown, solve the problem that is sending Peppermint Patty into an agitated state. How much cream and how much milk, to the nearest hundredth of a gallon, must be mixed together to obtain 50 gallons of cream that contains 12.5% butterfat?

Exercises 3542 involve mixtures. The manager of a candystand at a large multiplex cinema has a popular candy that sells for $1.60 per pound. The manager notices a different candy worth $2.10 per pound that is not selling well. The manager decides to form a mixture of both types of candy to help clear the inventory of the more expensive type. How many pounds of each kind of candy should be used to create a 75-pound mixture selling for $1.90 per pound?

Exercises 3542 involve mixtures. A grocer needs to mix raisins at $2.00 per pound with granola at $3.25 per pound to obtain 10 pounds of a mixture that costs $2.50 per pound. How many pounds of raisins and how many pounds of granola must be used?

Exercises 3542 involve mixtures. A coin purse contains a mixture of 15 coins in nickels and dimes. The coins have a total value of $1.10. Determine the number of nickels and the number of dimes in the purse.

Exercises 3542 involve mixtures. A coin purse contains a mixture of 15 coins in dimes and quarters. The coins have a total value of $3.30. Determine the number of dimes and the number of quarters in the purse.

Exercises 4348 involve motion. When a small plane flies with the wind, it can travel 800 miles in 5 hours. When the plane flies in the opposite direction, against the wind, it takes 8 hours to fly the same distance. Find the rate of the plane in still air and the rate of the wind.

Exercises 4348 involve motion. When a plane flies with the wind, it can travel 4200 miles in 6 hours. When the plane flies in the opposite direction, against the wind, it takes 7 hours to fly the same distance. Find the rate of the plane in still air and the rate of the wind.

Exercises 4348 involve motion. A boats crew rowed 16 kilometers downstream, with the current, in 2 hours. The return trip upstream, against the current, covered the same distance, but took 4 hours. Find the crews rowing rate in still water and the rate of the current.

Exercises 4348 involve motion. A motorboat traveled 36 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 2 hours. Find the boats rate in still water and the rate of the current.

Exercises 4348 involve motion. With the current, you can canoe 24 miles in 4 hours. Against the same current, you can canoe only 34 of this distance in 6 hours. Find your rate in still water and the rate of the current.

Exercises 4348 involve motion. With the current, you can row 24 miles in 3 hours. Against the same current, you can row only 23 of this distance in 4 hours. Find your rowing rate in still water and the rate of the current.

Describe the conditions in a problem that enable it to be solved using a system of linear equations.

Use Figure 4.11 on page 307 to write a word problem similar to Example 1 or Check Point 1 that involves the leisure activity of reading. Then solve the problem.

Exercises 1720 involve using systems of linear equations to compare costs of telephone plans and plans at a discount warehouse. Describe another situation that involves choosing between two options that can be modeled and solved with a linear system.

Describe two similarities between interest and mixture problems.

Must the concentration of a mixture always be greater than the concentration of an ingredient in one of the solutions and less than the concentration of the ingredient in the other solution being mixed? Explain your answer.

In Exercises 5457, determine whether each statement makes sense or does not make sense and explain your reasoning. The Sea Drift Hotel charges $650 for 7 nights and 10 meals, so I modeled these conditions using 7n 10m 650, where n is the cost of one night and m is the cost of one meal.

In Exercises 5457, determine whether each statement makes sense or does not make sense and explain your reasoning. A telephone calling plan charges $4 per month plus 7 per minute, so I modeled these conditions using y 0.07 4x, where y is the monthly charge when x minutes of calls are made.

In Exercises 5457, determine whether each statement makes sense or does not make sense and explain your reasoning. The perimeter of the large rectangle shown in the figure is 58 meters, so I modeled this condition using 2(x 8) 2(y 10) 58. 8 x 5 y 5

In Exercises 5457, determine whether each statement makes sense or does not make sense and explain your reasoning. Angles A and B are supplementary, so I modeled this condition using 4x 2y 4 12x 6y 12 180. B: 12x + 6y + 12 A: 4x 2y + 4

A set of identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. One twin tells you of a lucky number pair: When I multiply my first lucky number by 3 and my second lucky number by 6, the addition of the resulting numbers produces a sum of 12. When I add my first lucky number and twice my second lucky number, the sum is 5. Which twin is talking?

Tourist: How many birds and lions do you have in your zoo? Zookeeper: There are 30 heads and 100 feet. Tourist: I cant tell from that. Zookeeper: Oh, yes, you can! Can you? Find the number of each.

Find the measure of each angle whose degree measure is represented with a variable.

One apartment is directly above a second apartment. The resident living downstairs calls his neighbor living above him and states, If one of you is willing to come downstairs, well have the same number of people in both apartments. The upstairs resident responds, Were all too tired to move. Why dont one of you come up here? Then well have twice as many people up here as youve got down there. How many people are in each apartment?

In Lewis Carrolls Through the Looking Glass, the following dialogue takes place: Tweedledum (to Tweedledee): The sum of your weight and twice mine is 361 pounds. Tweedledee (to Tweedledum): Contrawise, the sum of your weight and twice mine is 362 pounds. Find the weight of each of the two characters.

You have $70,000 to invest. Part of the money is to be placed in a certificate of deposit paying 8 per year. The rest is to be placed in corporate bonds paying 12 per year. If you wish to obtain an overall return of 9% per year, how much should you place in each investment?

Select any two problems that you solved from Exercises 526. Use a graphing utility to graph the system of equations that you wrote for that problem. Then use the TRACE or INTERSECTION feature to show the point on the graphs that corresponds to the problems solution.

Solve: 2(x 3) 24 2(x 4). (Section 2.3, Example 3)

Simplify: 5 6(x 1). (Section 1.7, Example 7)

Write the slope-intercept form of the equation of the line passing through (5, 6) and (3, 10). (Section 3.5, Example 2)

Exercises 6870 will help you prepare for the material covered in the next section. If x 3, y 2, and z 3, does the ordered triple (x, y, z) satisfy the equation 2x y 4z 8?

Exercises 6870 will help you prepare for the material covered in the next section. Consider the following equations: 5x 2y 4z 3 Equation 1 3x 3y 2z 3. Equation 2 Eliminate z by copying Equation 1, multiplying Equation 2 by 2, and then adding the equations.

Exercises 6870 will help you prepare for the material covered in the next section. Write an equation involving a, b, and c based on the following description: When the value of x in y ax2 bx c is 4, the value of y is 1682. GROUP