Riley is planning to plant a lawn in his yard. He will need 9 pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs $3.50 per pound. How much of each seed should he buy so that the overall cost will be $4.02 per pound?

Given that total number of pounds of grass seed needed = 9

Let number of pounds of Bermuda seeds used = x

Let number of pounds of Fescue seeds used = y

Then sum of both gives equation:

x+y=9

or y=9-x ... (i)

Given that cost of 1 pound of Bermuda seed = $4.80

Then cost of x pound of Bermuda seed = $4.80x

Given that cost of 1 pound of Fescue seed = $3.50

Then cost of y pound of Fescue seed = $3.50y

total cost will be 4.80x+3.50y

Given that cost of 1 pound of mix seed = $4.02

Then cost of 9 pound of mix seed = $4.02*9

combining all three parts, we get equation:

4.80x+3.50y=4.02*9

4.80x+3.50y=36.18 ... (ii)

plug (i) into (ii)

4.80x+3.50y=36.18

4.80x+3.50 (9-x) = 36.18

4.80x+31.5-3.50x=36.18

4.80x-3.50x=36.18-31.5

1.3x=4.68

x=3.6

Now plug x=3.6 into (i)

y=9-x=9-3.6=5.4

Hence final answer is given by:

Let number of pounds of Bermuda seeds he should buy = 3.6 pounds

Let number of pounds of Fescue seeds he should buy = 5.4 pounds