How many pounds of nails costing $7 per pound must be mixed with 6 pounds of nails costing $3 per pound to yield a mixture costing $4 per pound?

How many pounds of nails costing $7 per pound must be mixed with 6 pounds of nails costing $3 per pound to yield a mixture costing $4 per pound?

Detailed Explanation

Let x = number of nails costing $7 per pound. The total cost of the mixture equals the sum of the cost for each type of nail or M = A + B, where A = 7x, B = 3(6), and M = 4(6 + x). Substitute the known values into the equation. 4(6 + x) = 7x + 18.

24 + 4x = 7x + 18

24 – 18 = 7x – 4x

3x = 6

x = 2

24 + 4x = 7x + 18

24 – 18 = 7x – 4x

3x = 6

x = 2