Question

Tim and Judy mix 2 kinds of feed for pedigreed dogs. They wish to make 29 pounds worth $0.68 per pound by mixing one kind worth $0.20 per pound with another worth $0.89 per pound. How many pounds of cheaper kind should they use in the mix? Round your answer to the nearest pound, if necessary.

A) 5 pounds of the cheaper kind
B) 10 pounds of the cheaper kind
C) 15 pounds of the cheaper kind
D) 20 pounds of the cheaper kind

Answer 1

By setting up a system of equations using the price and weight of each type of feed and solving for x, we find that Tim and Judy should use approximately 9 pounds of the cheaper feed, rounded to the nearest pound.

Step-by-step explanation:

To determine how many pounds of the cheaper kind of feed Tim and Judy should use in the mix, we can set up a system of equations based on the value of each type of feed and the total desired weight and value of the mix.

Let x be the amount of the cheaper feed and y be the amount of the more expensive feed. The following equations represent the total weight and total cost:

• x + y = 29 (total weight of the mix)
• (0.20x) + (0.89y) = 29 * 0.68 (total cost of the mix)

Solving this system of equations will give us the values of x and y.

Substitute y from the first equation into the second equation:

• (0.20x) + (0.89*(29-x)) = 19.72

Simplify and solve for x:

• 0.20x + 25.81 - 0.89x = 19.72
• -0.69x = -6.09
• x = 6.09 / 0.69
• x ≈ 8.826 pounds

After rounding to the nearest pound, Tim and Judy should use 9 pounds of the cheaper kind.