Nuts costing $9 per kg are to be mixed with nuts costing $6.5 per kg to make 10kg of nuts costing $8 per kg. How many kg of nuts costing $9 per kg should be used?
Let x be the number of kg of $9 nuts to be used, and y be the number of kg of $6.50 nuts to be used.
we want the total to be 10 kg, hence we have
x + y = 10 ........................(1)
we want the cost to be $8 per kg, since the cost of the x-nuts is 9x and the cost of the y-nuts is 6.5y, and the cost of the 10 kg mixture is to be $80, we also have the equation
9x + 6.5y = 80 ...................(2)
so now you have a system of two equations with two unknowns. Solve this system for x to get your answer.