Page 2 Mixture Problems 1 ) Jessica needs 4 lb of metal with 36 % silver. If Jessica combines one metal with 10 % silver, and another with 79 %

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1 Page 1 Part 1 Percent Change 1. A local cable television company currently charges $36 per month. It plans an increase in its monthly charge by 15%. What will the new rate be? ($41.40) 2. In 1980, the median age of U.S. residents was 30 years. By 1996, the median age had increased by about 15.3%. What was the median age in 1996? (34.59) 3. In 1995, the death rate per 100,000 U.S. residents from major cardiovascular disease was 174.4, which is about a decrease from What was the 1980 death rate per 100,000 from major cardiovascular disease? (255.53) 4. A worker s take-home pay was $480 after deductions totaling 40%. What is the worker s gross pay? ($800) 5. A cereal company advertises that its 16-ounce cereal represents 25% more than before. What was the original amount? (12.8) 6. A couple does not wish to spend more than $45 for dinner at their favorite restaurant. If a sales tax of is added to the bill and they plan to tip 15% after the tax is added, what is the most they can spend for the meal? ($36.40) 7. A discount store prices its blank videotapes by raising the wholesale price by 40% and adding $0.20. What must the tape s wholesale price be if the tape sells for $3.00? 8. Adams Clothing Store buys coats for $50 and then sells them for $80. What is the percent of mark up on the price of the coat? (60%) 9. Asabi s average in Math for the first nine weeks was an 88. His second nine weeks average decreased 12.5%. What was his average for the second nine weeks? (77) 10. In 1967, a 30-second Super Bowl commercial cost $40,000. In 2000, a 30-second commercial cost $1,800,000. What was the percent of change in the cost of a commercial? (4500%) 11. A manufacturing company with 450 employees begins a new product line and must increase their number of employees by 18%. How many total employees does the company now have? (531) 12. Marlis had 765 cards in her baseball collection. She sold 153 of the cards to purchase a new ipod. What is the percent of change in the number of Marlis baseball card collection? (20%) 13. Jenni, an employee of Hollister, bought a sweater originally priced at $55 for $38.50 after her employee discount. What percent off is the employee discount? (30%) 14. The World Future Society predicts that by the year 2020, airplanes will be able to carry 1400 passengers. Today s biggest jets can carry 600 passengers. What will be the percent of increase of airplane passengers? (233.3%) 15. In 1995, America Online had about 3,000,000 users. Over the next decade, users are expected to increase from a few million to the tens of millions. Suppose the number of users increases by 150% by the year How many users will there be in the year 2000? (7,500,000) 16. Music Systems, Inc. allows a 10% discount if a purchase is paid for within 30 days. An additional 5% discount is given if the purchase is paid for within 15 days. Brent Goodson buys a sound system that originally cost $360. If he pays the entire amount at the time of purchase, how much does he pay for his system after the successive discounts? ($307.80) 17. As soon as a new car is purchased and driven away from the dealership, it begins to lose its value, or depreciate. Alonso bought a 1994 Plymouth Neon for $9559. One year later, the value of the car was $8500. What was the percent of decrease of the value of the car? (11.07%)

2 Page 2 Mixture Problems 1 ) Jessica needs 4 lb of metal with 36 % silver. If Jessica combines one metal with 10 % silver, and another with 79 % silver, how much of each metal does Jessica need? 1.51 lb of 79 % 2.49 lb of 10 % 2 ) Mike mixed 13 L of cranberry juice into 9 L of apple juice, that had 56 % sugar. If the cranapple mixture was 32 % sugar, what was the percent of sugar in the cranberry juice? % 3 ) Tim has two bags of nuts; one with 78 % peanuts, and the other with 9 % peanuts. To make a 12 lb bag of 57 % peanuts, how much of each should Tim use? 6.96 lb of 78 % 5.04 lb of 28 % 4 ) How many g of gold should a coin of 35 % gold be if when combined with a 10 g pure gold necklace, it forms a metal that is 68 % gold? 9.70 g 5 ) Alyssa's trail mix was made combining 6 lbs of peanuts that cost 6 $/lb, 3 lbs of raisins at 5 $/lb, and 11 lbs of cashews at 3 $/lb. What was the cost per lb of the mixture? 4.20 $/lb 6 ) Jason mixed 10 oz of soil containing 19 % clay with 7 oz of soil with 12 % clay. What is the clay content in the mixture? % 7 ) Mary mixed 12 ml of a acidic solution with 8 ml of a 57 % acidic solution, to make a 52 % acidic solution. Find the percent acid concentration of the first solution % 8 ) Jessica dumped 8 lbs of a bag of apples with 49 % red apples, into a bag of 13 lbs which contained 52 % red apples. What is the new percent of red apples? % 9 ) Mike mixed 14 ml of a salt solution with 8 ml of a 48 % salt solution, to make a 43 % salt solution. Find the percent salt concentration of the first solution % 10 ) A 3 L solution that was 25 % vinegar was mixed with a 13 L solution that was 74 % vinegar. Find the new concentration of vinegar %

3 Page 3 Mixture Problems 1) Five hundred tickets were sold for a fundraising dinner. The receipts totaled $ Adult tickets were $7.50 each and children s tickets were $4.00 each. How many tickets of each type were sold? (375,125) 2) Twelve gallons of regular unleaded gasoline plus 8 gallons of premium unleaded gasoline cost $ Premium unleaded gasoline costs $0.11 more per gallon than regular unleaded. Find the price per gallon for each grade of gasoline. ($2.499, $2.609) 3) How many liters of a 20% acid solution must be mixed with a 60% solution to obtain 40 liters of a 35% solution? (25, 15) 4) Ten pounds of mixed nuts sells for $6.87 per pound. The mixture is obtained from two kinds of nuts, peanuts priced at $5.70 per pound and cashews at $8.70 per pound. How many pounds of each variety of nut are used in the mixture? (3.9, 6.1) 5) A truck travels for 4 hours at an average speed of 42 miles per hour. How much longer must the truck travel at an average speed of 55 miles per hours so that the average speed for the total trip will be 50 miles per hour? (6.4 hrs, or 6 hrs 24 minutes) 6) A mixture of nickels and quarters totals $9.90. There is a total of 50 coins. How many are quarters and how many are nickels? (37, 13) 7) The total score in a basketball game was 92 points. This was a combination of 2 point shots and 3 point shots. There were a total of 43 scoring events. How many were 2 point shots and how many were 3 point shots? (37, 6) 8) In a math class a grade was assigned for a combination of homework and quizzes. A student had an overall homework/quiz average of His quiz average was 78 and his homework average was 87. There were a total of 20 homework and quizzes assigned. How many were homework and how many were quizzes? (14, 6) 9) In a pen at Old MacDonald s farm there are some sheep and some geese. There is a total of 115 animals, and there are 424 legs. How many sheep and how many geese are there? (97, 18) 10) A materials scientist has 6 lbs of a 40% silver alloy. How many pounds of pure silver must he mix with the entire 6 pounds of 40% alloy to obtain as much of a 62% alloy as he can? (3.47 lbs) 11) Brian had 5 times as many quarters as dimes. If the total value of her coins was $16.20, how many of each kind of coin did she have? (12d, 60q) 12) Jenny received $6.10 in tips one afternoon. All of her tips were in quarters, dimes and nickels. There were five less dimes than quarters and seven less nickels than dimes. How many of each kind of coin was there? (6n, 13d, 18q) 13) Grant s change rack contained $8.80 in quarters, dimes and nickels. There were two more than five times as many nickels as quarters and four less than twice as many dimes as quarters. How many of each kind of coin was there in the change rack? (13q, 67n, 22d) 14) Trisha has a bag with 32 dimes and nickels worth $2.80. How many of each coin does she have? (8n, 24d) 15) Pasha has a box with 40 coins consisting of dimes, quarters and nickels that are worth $5.25. There are 5 more nickels than quarters. How many of each coin does she have? (15q, 20n, 5d)

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6 Page 6 D=RT 1) Darryl left the White House and traveled toward the ferry office at an average speed of 25 mph. Some time later Jacob left traveling in the opposite direction with an average speed of 35 mph. After Darryl had traveled for four hours they were 170 mi. apart. How long did Jacob travel? (2 HR) 2) A diesel train left the station at the same time as a freight train. The trains traveled in opposite directions. The freight train traveled at a speed of 34 mph. After 13 hours they were 793 mi. apart. How fast did the diesel train travel? (27 mph) 3) An aircraft carrier left the Dania Pier and traveled west at an average speed of 15 km/h. Some time later a fishing boat left traveling in the same direction but at an average speed of 20 km/h. After traveling for three hours the fishing boat caught up with the aircraft carrier. Find the number of hours the aircraft carrier traveled before the fishing boat caught up. (1 hr) 4) An Air Force plane left London and flew north at an average speed of 200 km/h. Some time later a cargo plane left flying in the same direction but at an average speed of 220 km/h. After flying for ten hours the cargo plane caught up with the Air Force plane. Find the number of hours the Air Force plane flew before the cargo plane caught up. (1 hr) 5) Abhasra left the White House and traveled toward the desert. Two hours later Julio left traveling at 35 km/h in an effort to catch up to Abhasra. After traveling for three hours Julio finally caught up. Find Abhasra's average speed. (21 mph) 6) Norachai left the mall and drove west at an average speed of 50 km/h. Chelsea left some time later driving in the opposite direction with an average speed of 20 km/h. After Norachai had driven for five hours they were 290 km apart. How long did Chelsea drive? (2 hr) 7) Huong made a trip to her cabin on the lake and back. The trip there took two hours and the trip back took three ours. She averaged 30 mph on the return trip. Find the average speed of the trip there. (45 mph) 8) Matt made a trip to his friend's house and back. On the trip there he drove 24 mph and on the return trip he went 30 mph. How long did the trip there take if the return trip took four hours? (5 hr) 9) A passenger plane left Tokyo and flew south. Two hours later a jet left flying at 275 mph in an effort to catch up to the passenger plane. After flying for nine hours the jet finally caught up. Find the passenger plane's average speed. (225 mph) 10) Ndiba drove to the ferry office and back. On the trip there he drove 30 km/h and on the return trip he went 45 km/h. How long did the trip there take if the return trip took two hours? (3 hr) 11) Kristin drove to the town hall and back. On the trip there she drove 50 km/h and on the return trip she went 60 km/h. How long did the trip there take if the return trip took five hours? (6 hr) 12) Perry left the airport one hour before Krystal. They traveled in opposite directions. Krystal traveled at 40 mph for four hours. After this time they were 385 mi. apart. What was Perry's speed? (75 mph) 13) A diesel train left Bangalore and traveled toward the repair yards at an average speed of 55 mph. A freight train left some time later traveling in the opposite direction with an average speed of 80 mph. After the diesel train had traveled for 17 hours the trains were 2295 mi. apart. How long did the freight train travel? (17 h) 14) An Air Force plane left Sydney and flew south at an average speed of 415 mph. A jet left some time later flying in the opposite direction with an average speed of 255 mph. After the Air Force plane had flown for six hours the planes were 3765 mi. apart. Find the number of hours the jet flew. (5 hr)

7 Pg 7 D=RT 17) An aircraft carrier left Port 59 and traveled toward St. Vincent at an average speed of 10 mph. A container ship left some time later traveling in the opposite direction with an average speed of 15 mph. After the aircraft carrier had traveled for three hours the ships were 75 mi. apart. How long did the container ship travel? 18) A submarine left Port 59 at the same time as a cruise ship. The vessels traveled in opposite directions. The cruise ship traveled at a speed of 15 km/h. After seven hours they were 140 km apart. How fast did the submarine travel? 19) Lea left the science museum three hours before Mike. They drove in opposite directions. Mike drove at 75 km/h for two hours. After this time they were 275 km apart. Find Lea's speed. 20) Jasmine left Perry's house and traveled north at an average speed of 40 km/h. Totsakan left some time later traveling in the opposite direction with an average speed of 80 km/h. After Jasmine had traveled for six hours they were 720 km apart. Find the number of hours Totsakan traveled. 21) An Air Force plane left Rome at the same time as a cargo plane. The planes flew in opposite directions. The cargo plane flew at a speed of 500 km/h. After three hours they were 2235 km apart. How fast did the Air Force plane fly? 22) An Air Force plane left the airport and flew toward Dublin. Two hours later a cargo plane left flying at 276 mph in an effort to catch up to the Air Force plane. After flying for ten hours the cargo plane finally caught up. Find the Air Force plane's average speed. 23) A freight train left Seoul and traveled toward the outer-most station. 12 hours later a diesel train left traveling at 30 mph in an effort to catch up to the freight train. After traveling for eight hours the diesel train finally caught up. What was the freight train's average speed? 24) Ryan left Jennifer's house and traveled toward the town hall at an average speed of 50 mph. Some time later Shreya left traveling in the same direction but at an average speed of 75 mph. After traveling for two hours Shreya caught up with Ryan. Find the number of hours Ryan traveled before Shreya caught up. answers 17) 3 hours 18) 5 km/h 19) 25 km/h 20) 6 hours 21) 245 km/h 22) 230 mph 23) 12 mph 24) 3 hours

8 Page 8 D=RT 1 ) Sally traveled to Atlanta by car. Going there took 6 hours, and the return trip lasted 5 hours. Sally averaged a speed of 67 mph while returning. Find the average speed of the trip there mph 2 ) Sally left the city traveling at 53 mph, while, at the same time, Jessica left the city going the opposite direction at a speed of 56 mph. Find the time Sally traveled before the two were 146 miles apart hours 3 ) A plane set off to Portland at a speed of 235 mph. On the return flight of 8 hours, the plane cruised at 270 mph. How many hours long was the flight to Portland? 9.19 hours 4 ) Mary left Atlanta traveling 48 mph. Keith, to catch up, left some time later driving at 57 mph. Keith caught up after 6 hours. How long was Mary driving before Keith caught up? 7.12 hours 5 ) Alyssa left the city for vacation. Sara left 9 hours later going 90 mph faster to catch up. After 8 hours Sara caught up. What was Alyssa's average speed? mph 6 ) A train left for Portland, and 8 hours later, a car traveling 42 mph tried catching up to the train. After 3 hours, the car caught up. What was the train's average speed? mph 7 ) A truck and van left from Burbank in opposite directions. The truck traveled for 6 hours at 67 mph. The vehicles were 677 miles apart. Find the van's average speed mph 8 ) A cargo plane flew from the US across the Atlantic at 260 mph, and flew back to the US at 280 mph. Given that the first trip took two hours longer, how long was the return trip? hours 9 ) Sally left Paris with a speed of 66 mph. Sara also left at the same time in the opposite direction at a speed of 43 mph. Find how many hours Sara must travel before they are 353 miles apart hours 10 ) Fred left downtown Paris, and three hours later, Tim left going 70 mph faster to catch up. After another two hours, Tim caught up. Find Fred's average speed mph

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12 Pg 12 Answers pg 9-11

13 Pg 13 Answers 1) 12 2) 617 3) 22 Answers 4)14 5) 50 6) 70 cents

14 Pg 14 Answers 7) 14 8) 12 9) 44 10) 10 Answers 11) plumber $25.50, apprentice $21 12) $7 13) 7 14) 9 17) $ ) Natalie 13N, dirk 9D, Quincy 4Q

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16 Pg 16 Answers: a) 1.36 hr, 75 mi b) Joe 4 mph, Tom 2, c) 67.5 mph d) 4 hr e) Smith 45 mph, White 42 mph f) 20 mph g) 1 st 3 mph, 2 nd 4 mph h) 8 min or 2/15 hr i) 600 mi j) 1080 mi k) mi