STEPS:
I. Read the problem carefully. Understand what is required.
II. Highlight important information.
III. Set up equation.
IV. Solve the problem.
V. Validate and check if your answer makes sense.
Handouts
LINK: Worded Problems
Topics:
Number Problem
Age Problem
Mixture Problem
Clock Problem
Variation Problem
Work Problem
Motion Problem
Interest Problem
Exercises
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1. A plane takes the same amount of time to fly 40 miles against the wind as it does to fly 50 miles with the wind. If the speed of the wind is 20 mph, determine the speed of the plane in still air. a. 160 mph b. 170 mph d. 190 mph 2. A motorboat can travel 10 mph in still water. If the boat takes the same amount of time to travel 5 miles upstream as it does to travel 6 miles downstream, find the speed of the current. a. 0.75 mph b. 0.62 mph c. 0.91 mph d. 0.53 mph 3. One racer can cycle 70 miles in the same time that another racer cycles 50 miles. If the first racer cycles 10 mph faster than the second, compute the speed of the slower racer. a. 20 mph b. 30 mph c. 35 mph d. 25 mph 4. The product of two consecutive even integers is 80, find the smaller integers. b. -8, -10 c. 8, 10 d. -8, 10 5. If the smaller of two consecutive integers is tripled, the result is 11 more than the larger. Find the integers. a. 5 b. 6 c. 7 d. 8 6. Two consecutive even integers have a sum of 58. Find the integers. a. 26 b. 27 c. 28 d. 29 7. The sum of two numbers is 55. One number is 5 more than the other. Find the numbers. a. 28 b. 29 c. 30 d. 31 8. A boat man rows to a place 5 miles with the stream and back in 15 hours, but finds he can row 12 miles with the stream in the same time as 2.5 miles against the stream. Find the rate of the stream. a. 0.421 mph b. 0.322 mph c. 0.633 mph d. 0.788 mph 9. One number is 6 less than the other. If the sum is 130, what are the numbers? a. 68, 62 b. 70, 64 c. 66, 60 d. 72, 66 10. Thrice the sum of two numbers is 33. The sum of the squares of two numbers is 61. The product of the two numbers is ____. a. 45 b. 40 c. 35 11. Furniture having 18% markdown sale. What was the original price of table whose sale price is P7000? a. P8211.6 c. P8010.0 d. P8790.5 12. A collection of 28 dimes and quarters is worth $3.85. How many quarters are there? a. 5 b. 8 c. 6 13. You see fireworks 3 seconds before you hear them. If the speed of sound is 1200 fps, how far away are the fireworks? a. 3300 ft b. 3500 ft c. 3600 ft d. 3200 ft 14. Two cyclist head in opposite directions on a straight road. One cycles at 12 mph and the other at16 mph. In how many hours will they be 74 miles apart? a. 2.6 sec b. 3.3 sec c. 4.2 sec d. 5.8 sec 15. Six times the sum of a number and 1 are 14 less than the number. Find the number. a. -5 b. -4 c. -6 d. -7 16. How many pounds of pure antifreeze should be mixed with 70 pounds of a 40% antifreeze solution to produce 50% antifreeze solution? a. 12 lbs b. 13 lbs c. 14 lbs d. 15 lbs 17. How many grams of an alloy that is 75% copper should be melted with 25 grams of an alloy that is 35% copper to produce an alloy that is 45% copper? b. 7-1/2 c. 6-3/4 d. 8.0 18. Alex is 6 years older than Mario. In 8 years the sum of their ages is 36. Find the present age of Alex. a. 10 b. 11 c. 12 d. 13 19. X and Y working together can finish painting a home is 7 days. X, working alone, can finish it in 4 days less than Y. How long will it take each of them to finish working alone? b. 16 and 12 days c. 20 and 18 days d. 22 and 16 days 20. A faucet can fill an empty utility sink 4 minutes. The drain can empty a full sink in 6 minutes. If by mistake both are open, how long will it take to fill an empty sink? a. 5-1/3 min b. 6-2/3 min c. 7-3/4 min d. 4-1/2 min 21. Luigi can type twice as fast as Susan. Together they can type the annual report in 5 days. How long would it take Luigi to type the annual report by herself? a. 5.5 days b. 6 days c. 6.5 days d. 7.5 days 22. Bryan can mow the lawn mower in 4 hours, Robert can mow the same lawn in 3 hours. How long would it take Bryan and Robert to mow the lawn? a. 3.8 hrs b. 4.5 hrs c. 2.1 hrs d. 1.7 hrs 23. A chemist of a distillery experimented on two alcohol solutions of different strength, 30% alcohol and 45% alcohol, respectively. How many cubic meters of each strength must be used in order toproduce a mixture 120 m3 that contains 43%, alcohol? a. 14 m3 b. 15 m3 c. 17 m3 d. 16 m3 24. A pump can pump out a tank 12 hours. Another pump can pump the same tank in 18 hours. How long will it take both pumps together to pump out the tank? a. 5.2 hrs b. 6.3 hrs c. 7.2 hrs d. 8.7 hrs 25. James is 5 years older than Ruby. In 6 years the sum of their ages is 35. Find the age of Ruby. a.8 b. 9 c. 10 d. 11 26. Dely is now twice as old as Tom. Four years ago, Dely was three times as old as Tom then. How old is Dely? a. 8 b. 9 c. 10 27. At what time after 12:00 noon will the hour hand and minute hand of the clock first form an angle of 120o? a. 12:30.88 b. 12:45.75 c. 12:18.42 28. How much water must be evaporated from 12 kg solution which has 5% salt to make a solution of 12% salt? a. 3 kg b. 4 kg c. 5 kg d.6 kg 29. What time after 10 o’clock will the hands of the clock be perpendicular for the second time? a. 10:32.73 b. 10:38.22 c. 10:36.50 d. 10:34.76 30. The product of two consecutive odd integers is 35. Find the smaller integer. a. 5 b. 6 c. 7 d. 8 31. If y varies directly as x, and y=5 when x=14, then find y when x=25. a. 7.21 b. 6.31 c. 8.93 d. 5.11 32. The force required to stretch a spring is directly proportional to its length. The force of 50 kN is needed to stretch a spring of 6 mm. If a force of 150 kN is applied, determine the length stretched. a. 16 mm b. 18 mm c. 20 mm d. 22 mm 33. If x varies directly as y and inversely as z, and x=18 when y=8 and z=3, find the value of x when y=15 and z=5. a. 20-1/3 b. 20-3/4 c. 20-1/2 34. Michael invests P1800 more at 9% than he invests at 13%. The interest from the two investments was P200. How much did she invest at 13% investment? a. P160.2 b. P178.5 c. P172.7 d. P168.4 35. Dory invested her income tax refund in two separate accounts. She invested part of it at 8% and triple that amount at 12%. The total first year interest from the two investments was P1200. How much does she invest at 8%? a. P2535.35 b.P2272.72 d. P2323.32 36. The length of a rectangle is 2 meters more than three times the width. The area of the rectangleis 35 m2. Find the length. a. 11.30 m b. 12.28 m c. 10.33 m d. 13.15 m 37. The length of a rectangle is 6 cm longer than the width. The area of the rectangle is 60 cm2. Find the width. a. 4.32 cm b. 5.31 cm c. 6.22 cm d. 3.56 cm 38. The perimeter of a small rectangular industrial lot is 150 m and its diagonal is 60 m. Find the area of the land. a. 1020.5 m2 b. 1121.3 m2 c. 1012.5m2 d. 1055.8 m2 39. Richard invests P2000 more at 8% than he invests at 15%. The interest from the two investments is the same. How much did she invest at 15%? a. P2200.5 b. P2328.1 c. P2501.5 d. P2285.7 40. The cost of renting a car is P350 per day plus P15 per mile. How many miles can you be driven in one day for a total cost of P500? a. 10 miles b. 11 miles c. 12 miles d. 13 miles 41. The length of rectangle is 6 meters less than three times the width. If the perimeter is 58 meters, find the width and length. b. 9.25 m and 22.35 m c. 7.32 m and 27.33 m d. 8.75 m and 26.22 m 42. In a right triangle one of the sides is five units longer than the other. The length of the hypotenuse is 60. Find the length of the shorter side. a. 32.8 m b. 34.3 m c. 38.8 m d. 30.2 m 43. If it takes 5 men to smoke 25 cigarettes in 30 minutes, how many sticks of cigarette will 12 men smoke in 2 hours? a. 120 b. 125 c. 130 d. 110 44. A salesperson makes a commission of P7000 in sales of P35,000. At the same rate, what commission would she make on sales of P183,000 a. P36600 b. P4550 c. P32300 d. P38800 |
