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This Lesson (Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts) was created by by ikleyn(52754)
  About ikleyn: Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanutsProblem 1A coffee shop has coffee which worth $6 per pound. They want to mix it with 20 pounds of coffee which worth $9 per pound to geta mixture that can be sold for $8 per pound. How many pounds of the cheaper coffee should they use? Solution Let x be the number of pounds of coffee worth $6 per pound what should be mixed. It costs 6*x dollars. 20 pounds of $9 coffee costs 9*20 dollars. In total, the mix costs 6x + 9*20 dollars. Hence, one pound of the mix costs Simplify and solve it: 6x + 180 = 7*(x+20), (after multiplying both sides by (x+20) ) 6x + 180 = 7x + 140, 180 - 140 = 7x - 6x, 40 = x. Answer. x = 40. 40 pounds of the $6 coffee should be mixed with 20 pounds of $9 coffee to get the mix at the price of $7 per pound. Problem 2Chocolate coffee beans sell for $7.00 per pound and hazelnut coffee beans sell for $6.10 per pound. One customer wantsa 6 pound mixture of both types of coffee. How many pounds of each should be used if the mixture is to cost $6.40 per pound? Solution Let c be the number of pounds of the chocolate coffee and h be the number of pounds of the hazelnut coffee to be mixed. So, your first equation is: c + h = 6 The cost of the mix should be 6*$6.40 = $38.40. From the other side, it is 7*c + 6.10*h. Thus you have the second equation 7*c + 6.10*h = 38.4. Now, you can solve this system of two equations by substitution. c = 6 - h, 7(6-h) + 6.1h = 38.4, 42 - 7h + 6.1h = 38.4, 42 - 0.9h = 38.4, -0.9h = -3.6, h = 4. c + 4 = 6. c = 2. Answer. 2 pounds of chocolate coffee and 4 pounds of hazelnut coffee should be used. Problem 3A customer has asked a caterer for 60 LB of nuts, 60% of which are to be cashews.The caterer has available mixtures of 70% cashews and 45% cashews. How many pounds of each mixture should be used? Solution The caterer needs to mix x lbs of the 70% cashew mixture with (60-x) lbs of the 45% cashew mixture to obtain the 60 lbs of 60% cashew mixture. Change the percentages to their decimal equivalents and write the algebraic equation to solve for x. 0.7*x + 0.45*(60-x) = 0.6*60. Simplify and solve for x. 0.7x + 27 - 0.45x = 36. Combine like-terms. 0.25x = 36-27, 0.25x = 9. Divide both sides by 0.25. x = 36. Answer. The caterer should mix 36 lbs of the 70% cashew mixture with (60-36 = 24) lbs of the 45% cashew mixture to obtain 60 lbs of 60% cashew mixture. Problem 4Peanuts sell for $3.00 per pound. Cashews sell for $6.00 per pound. How many pounds of cashews should be mixedwith 12 pounds of peanuts to obtain a mixture that sells for $4.20 per pound? Solution Let x be the number of pounds of cashews to be mixed. So, the weight of the mix is 12 + x pounds. The cost of the mix should be 12*$4.20 = $50.40. From the other side, it is 12*3 + 6.00*x dollars. Thus you have an equation 12*3 + 6.00*x = 50.40. Simplify and solve the equation: 6x =50.40 - 36, 6x = 14.40, x = Answer. 2.4 pounds of cashews should be used. My other lessons on word problems for mixtures in this site are - Mixture problems - More Mixture problems - Solving typical word problems on mixtures for solutions - Word problems on mixtures for antifreeze solutions - Word problems on mixtures for dry substances like candies, dried fruits - Word problems on mixtures for dry substances like soil and sand - Word problems on mixtures for alloys - Typical word problems on mixtures from the archive - Advanced mixture problems - Advanced mixture problem for three alloys - Unusual word problem on mixtures - Check if you know the basics of mixtures from Science - Special type mixture problems on DILUTION adding water - Increasing concentration of an acid solution by adding pure acid - Increasing concentration of alcohol solution by adding pure alcohol - How many kilograms of sand must be added to a mixture of sand and cement - Draining-replacing mixture problems - How much water must be evaporated - Advanced problems on draining and replacing - Using effective methodology to solve many-steps dilution problems - Entertainment problems on mixtures - OVERVIEW of lessons on word problems for mixtures Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I. This lesson has been accessed 8487 times. |
