Megan bought x pounds of coffee in which cost $3 per pound and 18 pounds of coffee at $2.50 per pound for the company picnic. Find out the total number of pounds of coffee purchased if the average cost per pound of both categories together is $2.85.
Let x = the amount of coffee at $3 per pound. Let y = the total amount of coffee purchased. If there are 18 pounds of coffee at $2.50 per pound, after that the total amount of coffee can be expressed as y = x + 18. Use the equation 3x + 2.50(18) = 2.85y because the average cost of the y pounds of coffe is $2.85 per pound. To solve, substitute y = x + 18 into 3x + 2.50(18) = 2.85y. 3x + 2.50(18) = 2.85(x + 18). Multiply on the left side and utilize the distributive property on the right side: 3x + 45 = 2.85x + 51.30. Subtract 2.85x on both sides: 3x - 2.85x + 45 = 2.85x - 2.85x + 51.30. Simplify: 0.15x = 45 51.30. Subtract 45 from both sides: 0.15x