MATEMÁTICAS_JVCJ

SOLVING PROBLEMS: SYSTEMS OF EQUATIONS

  1. The sum of two numbers is - 42. The first number minus the second is 52. What are the numbers?
  1. One day a store sold 30 sweatshirts. White ones cost $10.95 and neon ones cost $18.50. In all, $419,10 worth of sweatshirts were sold. How many of each color were sold?
  1. The perimeter of an NBA basketball court is 288 ft. The length is 44 ft longer than the width. Find the dimensions.
  1. Two angles are complementary. The sum of the measure of the first angle and half the second angle is 64°. Find the measures of the angles.
  2. A basketball player scored 18 times during one game. He scored a total of 30 points, two for each field goal and one for each free throw. How many field goals did he make? How many free throws?
  1. Hockey teams receive two points when they win and one point when they tic. One season, a team won a championship with 60 points. They won fine more games than they tied. How many wins and how many ties did the team have?
  1. The difference between two numbers is 11. Twice the smaller plus three times the larger is 123. What are the numbers?
  1. At a summer playhouse, 343 tickets were sold. Adults’ tickets cost $6.50 and children’s tickets cost $4.00. In all, $2099.50 was taken in. How many of each kind of ticket were sold?
  1. The perimeter of a standard tennis court, when used for doubles play, is 228 ft. The width is 42 ft less than the length. Find the dimensions.
  1. Two angles are supplementary. One angle is 3° less than twice the other. Find the measures of the angles.
  1. At a barbecue, there were 250 dinners served. Children’s plates were $350 each and adults’ plates were $7.00 each. If the total amount of money collected was $1337, how many of each type of plate was served?
  1. An airplane has a total of 152 seats. The number of coach-class seats is 5 more than six times the number of first-class seats. How many of each type of seat are there on the plane?
  1. A disc Jockey must play 12 commercial spots during 1 hr of a radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 mm, how many 30-sec commercials were played that hour? How many 60-sec commercials?
  1. The difference between two numbers is 16. Three times the larger number is nine times the smaller. What are the numbers?
  1. Soybean meal is 16% protein; cornmeal is 9% protein. How many pounds of each should be mixed together in order to get a 350-lb mixture that is 12% protein?
  1. One canned juice drink Ls 15% real orange juice; another is 5% real orange juice. How many liters of each should be mixed together in order to get 10 L that is 10% real orange juice?
  1. Two investments are made totaling $8800. For a certain year, these investments yield $524 in simple interest. Part of the $8800 is invested at 7% and part at 5%. Find the amount invested at each rate.
  1. $3270 is invested, part of it at 6% and part of it at 8.5%. The total yield is $225.45. How much was invested at each rate?
  1. A lumber company can convert logs into either lumber or plywood. In a given day, the mill turns out a total of 400 units of lumber and plywood. It makes a profit of $20 on a unit of lumber and $30 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $11,000?
  1. The sum of two numbers is - 63. The first number minus the second is - 41. What are the numbers?
  1. A chemist has one solution that is 25% boric acid and a second that is 50% boric acid. How many liters of each should be mixed together in order to get 10 L of a solution that is 40% boric acid?
  1. Antifreeze A is 18% alcohol; antifreeze B is 10% alcohol. How many liters of each should be mixed in order to get 20 L of a mixture that is 15% alcohol?
  1. Two investments are made totaling $15,000. For a certain year, these investments yield $1432 in simple interest. Part of the $15,000 is invested at 9% and part at 10%. Find the amount invested at each rate.
  1. $27,000 is invested, part of it at 4.5% and part of it at 8%. The total yield is $1547.50. 110w much was invested at each rate?
  1. At a baseball concession, three hot dogs and five hamburgers cost $18.50. Five hot dogs and three hamburgers cost $16.70. Find the cost of one hot dog and the cost of one hamburger.
  1. Hannah is twelve years older than her brother Irving. Four years from now, Irving will be two-thirds as old as Hannah will be four years from now. How old are they now?
  1. A student makes a $9.25 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?
  1. A camper gets on an interstate highway and sets its cruise control the a speed of 55 mph. Three hours later, a car gets un the same interstate at the same place and sets its cruise control to a speed of 65 mph. After what distance will the car overtake the camper?
  1. A motorboat took 3 hr to make a downstream trip with a 6-mph current. The return trip against the same current took 5 hr. Find the speed of the boat in still water.
  1. A salesperson is late for a meeting after traveling from one town to another at a speed of 32 mph. If she had gone 4 mph faster, she could have made the trip in 1/2 hr less time. How far apart are the towns?
  1. Al the circus, five sodas and four boxes of popcorn cost $19.90. Four sodas and five boxes of popcorn cost $19.25. Find the cost of one soda and the cost of one box of popcorn.
  1. Carlos is eight years older than his sister Maria. Four years ago, Maria was two-thirds as old as Carlos was four years ago. How old are they new?
  1. A customer goes to a bank and gets change for a $50 bill consisting of ah $5 bills and $1 bills. There are 22 bills in all. How many of each kind are there?
  1. Two angry motorists leave a collision site at the same time traveling in opposite directions. One car travels at 80 km/h and the other at 96 km/h. In how many hours will they be 528 km apart?
  1. A canoeist paddled for 4 hr with a 6-km/h current to reach a campsite. The return trip against the same current took 10 hr. Find the speed of the canoe in still water.
  1. A pilot computes his flight time against a head wind for a trip of 2900 mi at 5 hr The flight would take 4 hr and 50 min if the head wind were half as great. Find the head wind and the plane’s air speed.
  1. Two planes travel toward each other from cities that are 780 km apart at rates of 190 km/h and 200 km/h. They started at the same time. In how many hours will they meet?
  1. Two airplanes start at the same time and fly toward each other from points 1000 km apart at rates of 420 km/h and 330 km/h. When will they meet?
  1. A piece of posterboard has a perimeter of 156 in. If you cut 6 in. off the width, the length becomes four times the width. What are the dimensions of the original piece of posterboard?
  1. A limited edition of a book published by a historical society was offered for sale to its membership. The cost was one book for $12 or two books for $20. The society sold 880 books and the total amount of money taken in was $9840. How many members ordered two books?
  1. An automobile gets 18 miles per gallon (mpg) in city driving and 24 mpg in highway driving. The car is driven 465 mi un a full tank of 23 gal of gasoline. How many miles were driven in the city and how many were driven en the highway?
  1. A particular training aircraft can fly for 3 hr at a speed of 120 mph on a full tank of fuel. The instructor always plans to return to the airport with 1/2 hr of reserve fuel. A training flight is scheduled to fly east against a head wind of 20 mph and return with the same wind velocity. How far should the instructor allow the student to fly?
  1. Two motorcycles travel toward each other from Chicago and Indianapolis, which are about 350 km apart, at rates of 110 km/h and 90 km/h. They started at the same time. In how many hours will they meet?
  1. A truck and a car leave a service station at the same time and travel in the same direction. The truck travels at 55 mph and the car at 40 mph. They can maintain CB radio contact within a range of 10 mi. When will they lose contact?
  1. Nancy jogs and walks to school each day. She averages 4 km/h walking and 8 km/h jogging. The distance from home to school is 6 km and she makes the trip in 1 hr. How far does she jog in a trip?
  1. The numerator of a fraction is 12 more than the denominator. The sum of the numerator and the denominator is 5 more than three times the denominator. What is the reciprocal of the fraction?
  1. Phil and Phyllis are siblings. Phyllis has twice as many brothers as she has sisters. Phil has the same number of brothers as sisters. How many girls and how many boys are in the family?
  1. A tank at an aquarium contains 2000 gal of seawater. The seawater is 7.5% salt. How many gallons, to the nearest gallon, of freshwater must be added to the tank so that the mixture contains only 7% salt?
  1. The sum of three numbers is 5. The first number minus the second plus the third is 1.The first minus the third is 3 more than the second. Find the numbers.
  1. In triangle ABC, the measure of angle B is 2° more than three times the measure of angle A. The measure of angle C is 8° more than the measure of angle A. Find the angle measures.
  1. In a recent year, companies spent a total of $8413 billion on newspaper, television, and radio and. The total amount spent on television and radio ads was only $2.6 billon more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was $5.1 billion more than what was spent en television ads. How much was spent on each form of advertising? (Hint: Let the variables represent numbers of billions of dollars.)
  1. The sum of three numbers is 26. Twice the first minus the second is 2 less than the third. The third is the second minus three times the first. Find the numbers.
  1. In triangle ABC, the measure of angle B is three times the measure of angle A. The measure of angle C is 30° greater than the measure of angle A. Find the angle measures.
  1. A recent basic model of a particular automobile had a cost of 92,685. The basic model with the added features of automatic transmission and power door locks was $14,070. The basic model with just air conditioning (AC) and power door locks was $13,580. A basic model with just AC and automatic transmission was $13,925. What was the individual cost of each of the three options?
  1. In triangle ABC, the measure of angle B is twice the measure of angle A. The measure of angle C is 80° more than that of angle A. Find the angle measures.
  1. People are becoming more aware of their cholesterol levels. Recent studies indicate that a child should ingest no more than 300 mg of cholesterol per day. By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child would ingest 302 mg of cholesterol. If the child ate 2 cupcakes and 3 slices of the same pizza, he or she would ingest 65 mg of cholesterol. By eating 2 eggs and 1 cupcake, the child would take in 567 mg of cholesterol. How much cholesterol is in each item?
  1. Repeat Exercise 9 but replace the Brussels sprouts with asparagus, for which one 180 g serving contains 50 calories, 5 g of protein, and 40 mg of vitamin C. How many servings of each food are required to satisfy the physician’s requirements? (Which meal would you prefer eating?)
  1. In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20° more than that of angle A. Find the angle measures.
  1. Tim, Ann, and Amy made a total bowling score of 575. Tim’s score was 15 more than Ann’s. Amy’s was 20 more than Ann’s. Find the scores.

16/11/18 07:55 P.M.