Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 29 pounds of feed worth $.61 per pound by mixing one kind worth $.19 per pound with another worth $.95 per pound. How many pounds of the cheaper kind should they use in the mix(round to the nearest whole number)
So we write the equations for the dog feed. We know that the total amount of dog food is 29 pounds so we say C + E = 29 (C is cheaper and E is expensive). We also know that the mixture of the two is worth $0.61 per pound, so we say (0.19C + 0.95E)/29 = 0.61. Find E by subtracting C from both sides of the first equation to get E = 29 - C. Plug this in to the other equation to get (0.19C + 0.95(29 - C))/29 = 0.61. Multiply both sides by 29 to get 0.19C + 0.95(29 - C) = 17.69. Distribute and add up the C's to get -0.76C + 27.55 = 17.69. Subtract and divide from both sides to get the answer C = 12.97 which rounds up to 13 pounds.