5-A5 Using Systems of Equations to Solve Word Problems Alg 1H

Transcription

1 5-A5 Using Systems of Equtions to Solve Word Problems Alg 1H system of equtions, solve the system using either substitution or liner combintions; then nswer the problem. Remember word problems need word nswers. 1. Two crs trveled in opposite directions from the sme strting point. The rte of one cr ws 20 km/h less thn the rte of the other cr. After 5 hours, the crs were 700 km prt. Find the rte of ech cr. 2. The length of rectngle is 7 cm more thn the width. The perimeter is 78 cm. Find the rectngle s dimensions. 3. A shopper pid $7.70 for 2 continers of milk nd 3 continers of pple juice. It would hve cost 60 cents more for 2 continers of pple juice nd 3 continers of milk. How much would it cost to buy one continer of ech? 4. How mny kilogrms of nuts worth $5 per kilogrm should be mixed with 6 kg. of nuts worth $9 per kilogrm to mke mix worth $6.50 per kilogrm? 5. Lizzie Borden receives n nnul income of $277 from investing one mount of money t 6% nd nother mount t 8%. If the investments were interchnged, her income would increse by $6. Find the mount she hs invested t 8%. 6. JoAnn s income from two stocks lst yer ws $620. One stock pys dividends t the rte of 7% nd the other stock t the rte of 9%. If she hs invested totl of $8000, how much is invested t 7%? 7. This yer, the totl number of dogs nd cts sold by the Animl Adoption Agency ws Lst yer, 420 more cts nd double the number of dogs were sold for totl of How mny of ech were sold this yer? Optionl Chllenge Problem In 1943, the Brooklyn Bridge ws 10 times s old s the Golden Gte Bridge. Tht sme yer, the difference in their ges ws 54 yers. Find the yer of completion for ech bridge. Don t forget there re lso textbook problems (see your Assignment sheet).

2 5-A6 Review: Methods of Solving Systems of Liner Equtions Alg 1H Do on seprte Pper. Show work netly. 1. Wht exctly is the solution to system of liner equtions? Explin! 2. Prove which ordered pir is solution of 4x 3y = 1? A. (2, 3) B. (-2, -3) C. (3, 2) D. (-3, -2) 3. Solve 2x + y = 5 if x nd y re whole numbers. 4. Solve 2x 3y = 9 for y in terms of x. Solve ech system by the substitution method. 5. y = 2 6. x + y = 8 7. y = 2x 8. x + y = 5 x + 3y = -1 x y = 4 x + y = 12 3x 2y = x = 2y m 3n = b = b = -5 2x 3y = 4 4m + 6n = 10 + b = b = -8 Solve ech system by the elimintion (liner combintion) method. 13. x + y = m + n = x y = k 5p = -5 x y = 2 m n = 8 2x + y = 4 6k 5p = x y = x + y = x + 2y = x 3y = -3 2x + 2y = -6 4x + 3y = -8 x 4y = 3 x + y = 6 For 23 24, first express ech eqution in stndrd form. 21. x + 3y = x + 7y = b 4 = x 4 + y = -4 2x + y = 6 2x 5y = b = -3 x + y 3 = 6 Write lbels, system of equtions then solve, ech of the following problems. 25. The sum of two numbers is 15, nd their difference is 3. Wht re the numbers? 26. There re 288 bots in the hrbor. Some re silbots; the rest re motorpowered. There re 92 more motor-powered bots thn silbots. How mny silbots re there? 27. Two numbers differ by 16. The sum of twice the greter nd three times the smller is 72. Find the numbers. 28. The sum of Ed s ge nd twice Jill s ge is 48. In 3 yers, the sum of their ges will be 39. How old re they now? 29. Mike hs 26 coins worth $5.30 in his pocket. If ll the coins re dimes nd qurters, how mny of ech kind of coin does he hve? 30. Solve problem #13 by the grphing method.

3 5-A8 Using Systems of Equtions to Solve Word Problems Alg 1H system of equtions, solve the system using either substitution or liner combintions, then nswer the problem. Remember word problems need word nswers. 1. If 800 ml of juice drink is 15% grpe juice, how much pure grpe juice should be dded to mke drink tht is 20% grpe juice? 2. How mny liters of wter must be evported from 20L of 30% slt solution to produce 50% solution? 3. The following milk products contin the following mounts of butterft: 1% milk is 1% butterft, crem is 9% butterft, nd whole milk is 4% butterft. How mny ounces of 1% milk nd crem would you hve to mix together to mke gllon (128 ounces) of whole milk? 4. How mny milliliters of wter must be dded to 60ml of 15% iodine solution in order to dilute it to 10% solution? 5. How mny liters of wter must be evported from 84 L of 5% slt solution to produce solution tht is 35% slt? 6. Wild rice sells for $6 per pound, nd plin rice sells for $1 per pound. A grocer wnts 10 pounds of mixture to sell for $2 per pound. How much of ech type of rice must be used? 7. How mny liters of pure ntifreeze must be dded to 30 L of 60% ntifreeze solution to obtin 75% solution? 8. How mny liters of wter must be evported from 80 L of 20% slt solution to produce 25% slt solution? 9. How mny liters of 30% cid solution must be dded to 80 L of 20% solution to produce 28% cid solution? 10. One type of ntifreeze is 40% glycol, nd nother type of ntifreeze is 60% glycol. How much of ech kind of ntifreeze should be mixed to mke 100 gllons of ntifreeze tht is 48% glycol?

4 5-A9 Using Systems of Equtions to Solve Word Problems Alg 1H system of equtions, solve the system using either substitution or liner combintions, then nswer the problem. Remember word problems need word nswers. 1. A plne goes 2000 miles in five hours flying ginst the wind. The sme plne tkes four hours to fly the sme distnce with the wind. Wht s the rte of the plne in still ir, nd the rte of the ir current? 2. A mn took three hours to go 24 miles downstrem, nd six hours to return the 24 miles upstrem. Wht ws the rte of the bot in still wter nd the rte of the current? 3. Flying with the wind, wonder Womn flew her ircrft 300 miles in five hours. To return the 300 miles, she took six hours, flying ginst the wind. Wht ws the rte of the superplne in still ir nd the rte of the ir current? 4. A womn took three hours to go 48 miles downstrem, nd six hours to return upstrem ll 48 miles. Wht ws the rte of the bot in still wter nd the rte of the current? 5. A smll plne cn fly 2400 km in 10 hours flying into the wind. With the wind behind it, the plne cn fly 3200 km in the sme time. Wht is the speed of the wind? 6. Alice cycles to Crl s house t 12 mph nd returns by cr t 36 mph. If the round trip tkes 1 hour, how fr from Crl does Alice live? 7. Pt biked 1 mile in 3 minutes with the wind t her bck, nd then she returned in 4 minutes riding ginst the wind. Wht ws the speed of the wind in miles per hour? 8. Meg is 20 yers younger thn Phillip. In three yers Phillip will be twice s old s Meg will be. How is ech now? 9. Flying ginst the wind, Mr. Trump s compny plne flew 450 miles from one irport to nother in 1½ hours. The return trip, with no chnge in the wind s speed or direction, took 1 ¼ hours. Wht ws the speed of the wind? 10. Two crs pss Exit 20 on the turnpike t 8:00 A.M. One cr is trveling north nd the other is trveling south t speed tht is 4 km/h fster thn the northbound cr. At 8:45 A.M. the crs re 117 km prt. Find the speed of the southbound cr.

5 5-A10 Liner Systems Word Problem Prctice Alg 1H ALL WORK IS THE BE SHOWN NEATLY ON BINDER PAPER. BE SURE TO LABEL THE VARIABLES AND WRITE AN ALGEBRAIC EQUATION OR SYSTEM OF EQUATIONS FOR EACH PROBLEM. REMEMBER TO CHECK THAT YOU HAVE ANSWERED THE QUESTION THAT WAS ASKED! 1. How mny liters of wter must be dded to 50 L of 30% cid solution in order to produce 20% cid solution? 2. Students working t refreshment stnd mix crnberry juice t 50 cents per liter nd pple juice t 35 cents per liter to mke 120 liters of fruit drink worth 40 cents per liter. How mny liters of ech did they use? 3. The Espernzs invested prt of their $8000 t 12% nd prt t 8%. If their nnul investment income is $825, how much is invested t ech rte? 4. The sum of two numbers is 66. If the smller number is subtrcted from two-thirds of the lrger number, the result is one-third the positive difference of the originl numbers. Find the numbers. 5. A squre house is 24 ft. long, nd the house is locted on lot tht is 50 ft. longer thn it is wide. The perimeter of the lot is 20 ft. more thn 5 times the perimeter of the house. Find the length of the lot. 6. In mth contest, ech tem is sked 50 questions. The tems ern 15 points for ech correct nswer nd lose 8 points for ech incorrect nswer. One tem finished with score of 566. How mny questions did this tem nswer correctly? 7. A rowbot cn trvel distnce of 66 km in 3 hours with the current. The rowbot cn trvel 33 km in 3 hours ginst the current. Find the rte (speed) of the current. 8. How mny liters of wter must be evported from 10 L of 40% slt solution to produce 50% solution? 9. A plne verged 1000 km per hour flying from LA to Csper, Wyoming, but hevy winds slowed its speed on the return trip to 600 km per hour. If the entire trip took 6 hours of flying time, find the distnce from LA to Csper. 10. A grocer mixes two types of nuts, Brnd A nd Brnd B. If the mix includes 4 kg of Brnd A nd 6 kg of Brnd B, the mix will cost $6.20 per kilogrm. If it includes 2 kg of Brnd A nd 8 kg of Brnd B, it will cost $5.60 per kilogrm. Find the cost per kilogrm of ech brnd.