Word Problem Samples

Transcription

1 Word Problem Samples I. Simple Interest Problems Marcia has a job as a financial advisor in a bank. She advised acustomer to invest part of his money in a money marke,t ftmd earning 12% simple interest and the rest in an investment fund earning 14% simple interest. The customer had $6000 to invest. If he earned $772 in interest in 1 year, how much did he invest in each fund? Equation:.12x +.14( X) = x =.14x = x-.14x = x = x x = 3400 Solution: $3400 invested at 12% and $2600 invested at 14%.

2 bo An amount of money is invested at 3% annual simple interest, and $2000 more than that amount is invested at 4%. The total, annual interest is $920. How much is invested at each rate? Investment 2 " Total x I x ~~]=l.04(x+2000) 2x+2000 I ~ l 920 Equation:.03x +.04(x ) = x+.O4x+80 = x = x =840.07x x =12000 Solution: $12,000 invested at 3% and $14,000 invested at 4%. I

3 IL Percent Mixture Problems Bryan s Pest. Control stocks a 7% solution of insecticide for lawns and also a 15% solution. How many gallons of each should be mixed to produce 40 gallons that is 12% insecticide? Weak Solution Strong Solution Mixture : I.12(40) Equation:.07x +.15(40- x) :.12(40).07x + 6-.I5x = x-.15x = x= x x=15 Solution: 15 gallons of the 7% insecticide solution must be mixed with 25 gallons of the 15% insecticide solution.

4 bo How many liters of pure alcohol must we add to 20 liters Of a 40% solution to obtain a 60% solution? Mixture x (x + 20) Equation:.40(20)+ 1.OOx =.60(x + 20) 8+x =.60x+12 x -.60x = x = 4.40x x =10 Solution: 10 liters of pure alcohol must be added.

5 How many gallons of a 12%-salt solution must be mixed with 6 gallons of a 20%-salt solution to obtain a 15%-salt solution? Equation:.12x =.15x x-.15x = x = x -.3 " x=lo Solution: 10 gallons of the 12%-salt solution must be added.

6 do A chef has one cheese that contains 45% fat and another cheese that contains 20% fat. How many grams of each cheese should she use in order to obtain 30.grams ofa cheese mixture that is 30% fat? 3O Equation:.20x +.45(30- x) =.30(30).20x x = 9.20x-.45x = x = x x=18 ISolution: 18 grams of the 20%-fat cheese must be combined with 12 grams of the 45%-fat cheese.

7 III. Value Mixture Problems Marcela has a collection of nickels, dimes, and quarters worth $ The number of dimes is 10 more than twice the number of nickels, and the number of quarters is 25 more than the number of dimes. How many coins of each kind does she have?.05x.lo(2x + lo).25[(2x ) Equation:.05x +.10(2x + 10)+.25[(2x +10)+ 25]: x +.20x c = x = x = x = 15.75x x = 20 Solution: 20 nickels, 50 dimes, and 75 quarters.

8 bo A grocer at a specialty store is mixing tea worth $6 per pound with tea worth $8 per pound. He wants to obtain 144 pounds of tea worth $7.50 per pound. How much of each tea should he use? Cheap Expensive Mixture x I 1 6 I=! 6~ 144-x! I 8 I =1 8(144-x) 144 -! x I 7.50 I= I 7.50(144) Equation: 6x + 8(144- x) = 7.50(144) 6x x =1080 6x-8x = x = -72-2x x = 36 I S olution: 36 pounds of the $6 tea must be combined with 108 pounds of the $8 tea.

9 Co The Delgado Community College production of The Music Man was a big success. For opening night, 410 tickets were sold. Students paid $3 each, while non-students paid $7 each. If a total of $1650 was collected, how many students and how many non-students attended? Total Equation: 3x+7(410,x)= x x = x - 7x = x = x x -4 x = 305 I Soluti0n: 305 students and 105 non-students attended the event.

10 A cashier has a total of 126 bills in fives and tens. The total value of the money is $840. How many of each type bill does he have? Equation: 5x+10(126-x)= 840 5x x = 840 5x-10x = x = x x=84 Solution: 84 five-dollar bills and 42 ten-dollar bills. ]

11 IV. Uniform Motion Problems go Mercedes starts jogging at 5 miles per hour. One-half hour later, Karen starts jogging on the same route at 7 miles per hour. How long will it take Karen to catch Mercedes? *When Karen catches Mercedes, they will both have traveled the same distance. Equation: 5(x+ ):7x 5x = 7x 5x - 7x = x x x = 1.25 ISolution: Karen will catch Mercedes in 1 hour and 15 minutes.

12 Two trains leave a city at the same time, one traveling east and the other traveling west. At the end of 9½ hours, they are 1292 miles apart. If the rate of the train traveling east is 8 miles per hour faster than the rate of the other train, find their rates. 9½ *The sum of the two distances will be 1292 miles. Equation: 9~(x+8)~-9~x =1292 9~x+76+9~x=1292 9~x 9~x= x= x x = 64 Solution: The westbound traintravels at 64 miles per hour. The eastbound train travels at 72 miles per hour.

13 Tyrone leaves city A on a moped traveling toward city B at 18 miles per hour. At the same time, Tina leaves city B on a bicycle traveling toward city A at 14 miles per hour. The distance between the two cities is 112 miles. How long will it take before Tyrone and Tina meet? X 112 *The sum of the distances will be 112 miles. Equation: 18x+14x= x=112 32x x=3.5 Solution: Tyrone and Tina will meet in 3 hours and 30 minutes.

14 Puzzle Problems a. If the smaller of two consecutive odd integers is doubled, the result is 7 more than the larger of the two integers. Find the two integers. next consecutive odd inte y x+2 Equation: 2x=(x+2)+7 2x=x+9 2x-x =9 x=9 Solution: The two numbers are 9 and 11. bo Find three consecutive integers such that the. sum of one-half of the smallest and one-third of the largest is one less than theother integer. x x + 1 x + 2 Equation: ~x + g(x + 2)=(x +l)-i x+ x+g=x 6(~zx + Nx + ~)= 6x 3x+2x+4=6x 5x+4=6x 5x- 6x = -4 -x ---4 x=4 Solution: The three numbers are 4, 5, and 6.

15 Co In a reforestation program, 1400 seedling trees were planted. Twice as many spruce as hemlocks were planted. The number of balsams planted was twenty more than triple the number of hemlocks. How many of each type of seedling was. planted? Equation: x + 2x + (3x + 20)=!400 x + 2x + 3x + 20 =1400 x + 2x + 3x = x=1380 6x 1380 = 6 6 x = 230 ISolution: There are 230 hemlocks, 460 spruces, and 710 balsams. Lynn and Judy are pooling their savings to rent acottage in Maine for a week this summer. The rental cost is $950. Lyrm.s family is joining them, so she is paying a larger part of the cost. Her share of the cost is $250 less than -twice Judy s. How much of the rental fee is each of them paying? Equation: x+(2x-250)=950 x+2x-250 = 950 x+2x = x =1200 3x x = 400 Solution: Judy s share of the rent is $400. Lylm s share of the rent is $550.

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