Question

Jayson is planning to plant a lawn in his yard. He will need 9. 5 pounds of grass seed. He wants to mix Bermuda seed that costs $ 5. 40 per pound with Fescue seed that costs $ 3. 35 per pound. How much of each seed should he buy so that the overall cost will be $ 3. 89 per pound

Answer 1

Bermuda Seed: 2.5 lbs
Fescue Seed: 7 lbs

Explanation:

Amount of grass to be seeded = 9.5 lbs

Let the amount of Bermuda seed used be B pounds and Fescue seed used be F pounds

The total of these two should be 9.5 pounds

Therefore
B + F = 9.5 (1)

Cost per pound for Bermuda seed = $5.40; cost for B lbs = 5.40B
Cost per pound for Fescue seed = $3.35; cost for F lbs = 3.35F
Total cost = 5.4B + 3.35F

The total cost of 9.5 lbs of the mixture is 9.5 x 3.89 = $36.96

∴ 5.4B + 3.35F = 36.96 (2)

Multiply (1) x 3.35

=> 3.35B + 3.35F = 3.35 x 9.5

=> 3.35B + 3.35F = 31.823 (s)

(2) - (3)
5.4B + 3.35F - (3.35B + 3.35F) = 36.96 - 31.83
5.4B + 3.35F - 3.35B - 3.35F = 5.13

5.4B - 3.35B = 5.13

2.05B =5.13

B = 5.13/2.05 = 2.5 pounds

Therefore from (1),

F = 9.5 - B = 9.5 - 2.5 = 7 pounds

Bermuda Seed: 2.5 lbs
Fescue Seed: 7 lbs