Description
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)
Explanation & Answer
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.