Mathacle. Level Number Name: Date:

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1 1 1.) A chemist has 10 milliliters of a solution that contains a 30% concentration of acid. How many milliliters of pure acid must be added in order to increase the concentration to 50%? 2.) A radiator contains 8 quarts of a mixture of water and antifreeze. If 40% of the mixture is antifreeze, how much of the mixture should be drained and replaced by pure antifreeze so that the resultant mixture will contain 60% antifreeze? 3.) Two cities are connected by means of a highway. A car leave city B at 1:00 p.m. and travels at a constant rate of 40 mi/hr toward city C. Thirty minutes later, another car leaves B and travels toward C at a constant rate of 55 mi/hr. If the lengths of the cars are disregarded, at what time will the second car reach the first car? 4.) Two trains start from the same point and travel in opposite directions. The northbound train average 45 mi/hr and starts 2 hr before the southbound train, which averages 50 mi/hr. How long after the northbound train starts will the trains be 470 mi apart? 5.) Mrs. Stuart invested part of $4200 at 7% and the rest at 7.5%. If her total income from these investments was $306, how much did she invest at each rate? 6.) An investment firm has $100,000 to invest for a client and decides to invest it in two stocks, A and B. The expected annual rate of return, or simple interest, for stock A is 15%, but there is some risk involved, and the client does not wish to invest more than $50,000 in this stock. The annual rate of return on the more stable stock B is anticipated to be 10%. Determine whether there is a way of investing the money so that the annual interest is $12,000.

2 2 7.) You have accepted a job for which your annual salary will be $57,860. This salary includes a year-end bonus of $500. You will be paid twice a month. What will your gross pay be for each paycheck? 8.) You have accepted a job that pays $8 an hour. You are told that after a two-month probationary period, your hourly wage will be increased to $9 per hour. What percent raise will you receive after the two-month period? 9.) Your family has an annual income of $175,000 and the following expenses: mortgage ($2500), car payment ($700), food ($485), utilities ($300) and credit cards ($500). The total value of the monthly expenses represents what percent of your family s income? 10.) A rectangular kitchen is twice as long as it is wide, and it perimeter is 84 feet. Find the dimensions of the kitchen. 11.) A plane is flying nonstop from Atlanta to Portland, a distance of about 2700 miles. After 1.5 hours in the air, the plane flies over Kansas City (a distance of 820 miles from Atlanta). Estimate the time it will take the plane to fly from Atlanta to Portland. 12.) To determine the height of the Aon Center Building (in Chicago), you measure the shadow cast by the building and find it to be 142 feet long. Then you measure the shadow cast by a four-foot post and find it to be 6 inches long. Estimate the height of the building. 13.) You invested a total of $10,000 at 4.5% and 5.5% simple interest. During one year, the two accounts earned a total of $ How much money did you invest in each account?

3 3 14.) A store has $30,000 of inventory in 13-inch and 19-inch color televisions. The profit on a 13-inch set is 22% and the profit on a 19-inch set is 40%, the profit for the entire stock is 35%. How much was invested in each type of television? 15.) A cylindrical can has a volume of 200 cubic centimeters and a radius of 4 cm. Find the height of the can. 16.) A water tank can be emptied by using one pump for 5 hours. A second smaller pump can empty the tank in 8 hours. If the larger pump is started at 1:00 pm, at what time should the smaller pump be started so that the tank will be emptied at 5:00 pm? 17.) A social club charters a bus at a cost of $900 to take a group of members on an excursion to Atlantic City. At the last minute, five people in the group decide not to go. This raises the transportation cost per person by $2. How many people went on the trip? 18.) A jeweler has three small solid spheres made of gold, of radius 2 mm, 3mm, and 4mm. He decides to melt them down and make just one sphere out of them. What will the radius of this larger sphere be? 19.) Henry and Irene working together can wash all the windows of their house in 1 hour 48 minutes. Working alone, it takes Henry 1 hour 30 minutes longer than Irene to do the job. How long does it take Henry to wash the windows alone?

4 4 20.) Jack, Kay and Lynn deliver advertising flyers in a small town. If each person works alone, it takes Jack 4 hours to deliver all the flyers, it takes Lynn 1 hour longer than Kay to deliver all the flyers. Working together, they can deliver all of the flyers in 40% of the time it takes Kay working alone. How long does it take Lynn to deliver all the flyers working alone? 21.) Candy and Isha share a paper route. It takes Candy 70 minutes to deliver all the papers, whereas Isha takes 80 minutes. How long does it take them to work together? 22.) It takes Josh 14 hours to repair a car s transmission. After he had worked for 7 hours, Anish began to help him. Together they finished the job in 3 more hours. How long would it take Anish to repair the car by himself? 23.) You are planning to start a small business that will require an investment of $90,000. You have found some people who are willing to share equally in the venture. If you can find three more people, each person s share will decrease by $2500. How many people will be investing? 24.) A group of friends decides to buy a vacation home for $120,000, sharing the cost equally. If they could find one more person to join them, each person s contribution would drop by $6,000. How many people are in the group? 25.) A large pond is stocked with fish. The fish population P is modeled by the formula: P = 3t + 10 t + 140, where t is the number of days since the fish were introduced into the pond. How many days will it take for the fish population to reach 500?

5 5 26.) Jack and Jill decide to exercise together by walking around a lake. Jack walks around the lake in 16 minutes and Jill jogs around the lake in 10 minutes. If Jack and Jill start at the same time and at the same place, and continue to exercise until they return to the stating point at the same time, how long will they be exercising? How many laps will Jill make? 27.) Two trains left the same station at 3:15pm and traveled in opposite directions. The E train averaged 130 mph. The A train s speed was 110 mph. At what time were the trains 600 miles apart? 28.) Two cars traveled in opposite directions form the same starting point. The rate of one car was 10 mph faster than the rate of the other car. After four hours the cars were 460 miles apart. Find each car s rate. 29.) A man drove to the mountains at 60 mph. He returned at 40 mph. the return trip took 2 hours longer than the trip to the mountains. How long was the round trip to the mountains and back? 30.) A bus left a station traveling 100 mph. A second train left two hours later and headed in the same direction at 125 mph If the first train left at 10:30 am, at what time did the second train overtake the first train? 31.) A girl cycled 20 miles to the beach. She returned cycling one mph faster. The total time for the round trip was 9 hours. Find the girl s rate for each part of the trip.

6 6 32. It took Dora the same time to drive 135 miles as it took Diego to drive 180 miles. Dora s speed was 15 mph slower than Diego s. How fast did Diego drive? 33. A boy cyclist and a girl cyclist are 10 miles apart and peddling towards each other. The boy s rate is 6 miles per hour and the girl s rate is 4 miles per hour. There is also a friendly fly s rate is 20 miles per hour, by the time the cyclists meet each other, how far has the fly flown? 34.) Rebecca has 38 ounces of a 55% boric acid solution, which she wants to dilute to a 38% solution. How much water should she add to the boric acid? 35.) Peanut butter costs two cents an ounce. Jelly costs three hundred sixty eight cents per pound. Jordan wants to make 4 pounds of peanut butter and jelly. If she wants the entire mix to cost $2.96, how many pounds of jelly should she use? 36.) Sally made two investments for a total amount of $1080. One investment is at 5% and the other at 7%. The annual simple interest from the 5% investment is $7.20 less than the interest from the 7% investment. How much money was invested at 7%. 37.) A rug is to cover two thirds of the floor area of an 8 m by 12 m room. The uncovered part of the floor is to form a strip of uniform width around the rug. Find the width of this strip.

7 7 38.) If an object is projected vertically upward with initial speed k, measured in meters 2 per seconds, its height in meters after t seconds is given by h = kt 4.9t. a.) A baseball is thrown vertically upward with initial speed of 490 m/s. How long does it take the ball to reach its greatest height? b.) If a baseball is thrown vertically upward with initial speed 24.5 m/s, how high does it go? 39.) A stunt man working on the set of a movie is to fall out of a window 100 feet above the ground. For the stunt man s safety, an air cushion 26 feet wide by 30 feet long by 9 feet high is positioned on the ground below the window. For how many seconds will the stunt man fall before he reaches the cushion? 40.) A commercial jet took off from Kansas City for San Francisco, traveling a distance of 2550 km at a speed of 800 km/h. At the same time a private jet left San Francisco, traveling at 900 km/h and bound for Kansas City. How long after takeoff will the jets pass each other? 41.) Wilma drove at an average speed of 50 mi/hr fro her home in Boston to visit her sister in Buffalo. She stayed in Buffalo 10 hours and, on the trip back, averaged 45 mi/hr. She returned home 29 hours after leaving. How many miles is Buffalo from Boston?

8 8 42.) Kiran drove from Tortula to Cactus, a distance of 250 mi. She increased her speed by 10 mi/hr for the 360 mile trip from Cactus to Dry Junction. If the total trip took 11 hours, what was her speed from Tortula to Cactus? 43.) At 3:00 p.m., a man 165 cm tall casts a shadow 132 cm long. At the same time, a tall building nearby casts a shadow 160 m long. How tall is the building? 44.) Two cities are connected by means of a highway. A car leaves city B at 1:00 p.m. and travels at a constant rate of 40 mi/hr toward city C. Thirty minutes later, another car leaves B and travels toward C at a constant rate of 55 mi/hr. If the lengths of the cars are disregarded, at what time will the second car reach the first car? 45.) A runner starts at the beginning of a runner s path and runs at a constant rate of 6 mi/hr. Five minutes later a second runner begins at the same point, running at a rate of 8 mi/hr and following the same course. How long will it take the second runner to reach the first? 2 46.) A model for the demand of widgets is: d = 3p p 160, where d is the number of widgets a manufacturer can sell at a price of p dollars each. At what price does the manufacturer reach its maximum demand?

9 9 47.) You sell computers and earn $50,000 salary plus a bonus. Your bonus is 1/20 of the amount by which your sales exceed $300,000. Find the amount of your sales must in order for you to earn a total of $60, ) How much pure water must be mixed with 2 pints of 70% developer to produce a mixture that is 27% developer? L 49.) The motion of the leg of a robot can be modeled by: t = 2π, where L is he 32 length of the robot s leg in feet and t is the number of seconds required for one complete swing. a.) How much time is required for the leg to swing if it has a length of 15 inches? b.) How long is the leg if the swing takes 1 second? ) If the demand d and the supply s for motorcycles are d = and s = 200 p 1160, p find the profit p in hundreds of thousands of dollars, at the equilibrium point when demand is equal to supply.

10 10 Answers: 1. 4mL 2. 8/3 3. 2:20pm 4. 6 h , Yes, there is a way % % X lb ft 13. $4125, $ , cm 16. 3:24PM people mm hours hours /3 hours ½ hours people people days min, 8 laps 27. 5:45pm mph, 62.5 mph hours 30. 8:30pm mph going, 5 mph back mph miles oz 35. ½ lb 36. $ m 38. a. 50 s, b m s h mi mi/h

11 m 44. 2:50 pm min 46. $ , pints 49. a sec, b ft 50. $700,000