Step 1 The problem asks for the number of milliliters of water to be added. Step 2 Let.1 = the number of milliliters of water to be added.

Transcription

1 Example 2 L An auto mechanic has 300 ml of battery acid solution that is 60% acid. He must add water to this solution to dilute it so thai it is only 459c acid. How much water should he add? Soiution Step 1 The problem asks for the number of milliliters of water to be added. Step 2 Let.1 = the number of milliliters of water to be added. 1 Total amount x % acid = Amount of acid Original solution 300 bo^k ' 0.60(3(X)l Water X 0% 0 New solution 300 f X 45% 0,45(300 + X) Step 3 Original amount of acid + added acid = new amount of acid 0.60(300) i-^("M) * X) Step ) = 43(300 + x) 18,000 = V 4500 = 45x 100 = X Siep 5 The check is left to you ml of water should be added Answer Examples 1 and 2 are really very much alike. You can see this in the charts and in Step 3 of each.solution. In fact, mixture problems arc similar to investment problems, coin problems, and certain distance problems. Oral Exercises Read each problem and complete the chart. Use the chart to give an equation to solve the problem. Do not solve. L The owner of the Fancy Food Shoppe wants to mix cashews selling at.s8 00/kg and pecans selling at S7.00/kg. How many kilograms of each kind of nut should be mixed to get 8 kg worth $7.25 kg? Cashews Pecans Mixture Number of kg x Price per kg = Total cost ^ jtg ex 3Ea 322 Chapter 7

2 2. A chemist has 40 ml of a solution thai is 50^ acid. How much water should he add to make a solution thai is 10% acid? : Original solution 4t> i so Water added X e ; 0 New solution \'0 3. If 80*} ml (>f a juice drink is IS";;- grape juice, how much grape juice should be added to make a drink that is 20'* grape juice? Total amount x % juice = Amount of juice Original drink \^ Juice added X ( vo icok \ New drink 4. A chemist mixes 12 L of a solution that is 45'??^ acid with 8 L of a solution that is 70% acid. What is the percent of acid of the mixture? 1st Solution 2nd Solution Mixture Total amount < % acid = Amount of acid l-x ^0 5. A grocer mixes 5 lb of egg noodles costing 80e,'lb with 2 lb of spinach noodles costing Sl.50.ih. What will the cost per pound of the mixture be? 65% Egg noodles Spinach noodles Number of lb x Cost per lb = Total cost / AD Mixture.r W., J ft. Susan drove lor 2 li at 85 Km'h and then for 3 h more at 95 knvh. What was her average speed for the entire trip? 1st part of trip 2nd part of trip Rate X Time = Distance Entire trip X 1 323

3 7. Sam invested S2000 at 5i% amiual interest and $3000 at 8i% annual interest. What percent interest is he earning on his total investment? Amoimt invested x Rate = Interest Investment A Investment B 3VOO.0 ooo[ ^J^) i-3oeo{f'^)' Total Investments 5' voo X 8. Gina has a pile of 50 dimes and nickels worth $'1.30 How many coin*; of each type does she have? Number of coins x Value per coin = Total value Dimes Nickels Collection 50 fo ^ -4) ^6 din^, Problems A 1-8. Solve the problems in Oral Exercises 1-8. Solve. 9. How many liters of water must be added to 50 L of a 30% acid solution in order to produce a 20% acid solution? 10. How many milliliters of water must be added lu 60 ml of a 15% iodine solution in order to dilute it to a 10% iodine solution? 11. A spice mi.kture is 25% thyme. How many grams of thyme must be added to 12 g of the mixture to increase the thyme content to 40%? 12. A grocer mixes two kinds of nuts. One kind costs S5.00/kg and the other S5.80'kg. How many kilograms of each type are needed to make 40 kg of a blend woith S.-^-SO/kg? 13. Joanne makes a mixture of dried fruits by mixing dried apples costing $6.00/kg with dried apricots costing $8.00/kg. How many kilograms of each are needed to make 20 kg of a mixture worth S7.20/kg? 14. A farm stand owner mixes apple juice and cranberry juice. How mirch should he charge if he mixes 8 L of apple juice selling for 45(i'L with 10 L of cranberry juice selling for $l.08,'l? 15. If you drive for 2 h at 80 knv'h, how fast must you drive during the ne.xt hour in order to have an average speed of 75 km/h? 324 Chapter 7 /5

4 16. If Sylvia works overtime, she is paid li times as much per hour as usual. After working her usual 40 h last week, she worked an additional 4 h overtime If.she made $552 last week, find her usual hourly wage. C B 17. A chemist wishes to mix some pure acid with.some water to produce 16 L of a solution that is 30% acid. How much pure acid and how much water should be mixed? 18. How many liters of water must be evaporated from 10 L of a 40% salt solution to produce a 50% solution? 19. How many liters of water must be evap<irated from 20 L of a 30% salt solution to produce a 50% solution? 20. A wholesaler has 100 kg of mixed nuts that sell for H.W/kg. In order to make the price more attractive, she plans to mix in some cheaper nuts worth.$3.20/kg. If thejvliolesaler wants to sell the mixture for $3.40/kg, how many kilograms of the cheaper nuts should be used? 21. A securities broker advised'a client to invest a total of $21,000 in bonds paying 12% interest and in certificates of deposit paying 5i% interest. The annual income from these irivestuienis was "S2250. Find out how much was invested at each rate. 22. A collection of 50 coins is worth S5.20. There are 12 more nickels than dimes, and the rest of the coins are quarters. How many coins of each type are in the collection? 23. (a) If you bike for 2 h at 30 km/h and for 2 h ;«20 km;'h. what is your average speed for the whole trip? (b) If you bike for 60 km at 30 kmh and rentm at 20 km/h, what is your average speed for the whole trip? 24. The ratio of nickels to dimes to quarters is 3:8:1. If all the coins were dimes, the amount of money would be the same. Show that there are infinitely many solutions to this problem. 25. A grocer wants to make a mixture of three dried fruits. He decides that the ratio of pounds of banana chips to apricots to dates should be 3:11, Banana chips cost $1.17/lb, apricots cost $3.00;Ib. and dates cost $2.30/lb. What is the cost per pound of the mixture? ^ Mixed Review Exercises Evaluate. 1. 9% of 60 -f 0.4% of What percent of 160 is 12? 2. What percent of 45 is 18? is \2\% of what number? Evaluate if a = 2. ft = 3. x = 5. and y = V b i + b 7. (9.t + v) 8,.n-^ 9. 2a + 5b 10. {x - b)- 325

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