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.