Question: word problem solving with two unknowns, using rate(time)=distance? A baker purchased 12lbs of wheat flour and 15lbs of rye flour for a total cost of $18.30.  A second purchase, at the same prices, included 15 lbs of wheat flour and 10lbs of rye flour.  The cost of the second purchase was $16.75.  Find the cost per pound of the wheat flour and of the rye flour.

Answer: Let w = price of wheat flour per pound\nLet r = price of rye flour per pound\n\nFirst we have to set up our system of equations.\n12w + 15r = 18.30\n15w + 10r = 16.75\n\nNow we will use substitution to solve for a variable.  \n12w + 15r = 18.30\nSubtract 12w from both sides.\n15r = 18.30 - 12w\nDivide both sides by 15.\nr = 1.22 - .8w\n\nNow we substitute r into the other equation.\n15w + 10r = 16.75\n15w + 10 (1.22 - .8w) = 16.75\n15w + 12.2 - 8w = 16.75\n7w + 12.2 = 16.75\n7w = 4.55\nw = .65\n\nNow we substitute w back into one of the equations to get r.\n12w + 15r = 18.30\n12(.65) + 15r = 18.3\n7.8 + 15r = 18.3\n15r = 10.5\nr = .7\n\nSo, wheat flour costs $0.65 per pound and rye flour costs $0.70 per pound.\n\n*********************************************************************\n\nNow we can check our answer in the other equation.\n\n15w + 10r = 16.75\n15(.65) + 10(.7) = 16.75\n9.75 + 7 = 16.75\n16.75 = 16.75\n\nWe are good! :)
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