The Grass Doctor

Hey math brains! Algebra Homework question?

I got some algebra homework and its on "weighted averages" but im totally stumped. I've tried other online resources to see if I could get help or try to understand but nothing so far seems to be much help. I was wondering if anyone could explain to me HOW to get the answer. The problem says: A nursery sells Kentucky Blue Grass seed for $5.75 per pound and Tall Fescue seed for $4.50 per pound. The nursery sells a mixture of the two kinds of seed for $5.25 per pound. Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds of the mixture. Step by step please because I feel like Cosmo trying to fit the square block into the circle. :(

Public Comments

1. k = amount of Kentucky 5 - k = amount of fescue 575k + 450(5 - k) = 525 • 5 575k + 2250 - 450k = 2625 125k = 2625 - 2250 do that subtraction then divide by 125
2. I did this the odd way. The difference in the price between K and TF is 1.25 a pound. Think of 1.25 as five quarters. The price they are charging for the mixed grass is 5.25 That is 75 cents more per pound than pure TF (3 quarters) and 50 cents less (two quarters) less than pure TF That means the mixture is 2/5 less than pure TF or 60% K and 40% TF The correct way is probably to do it this way: K= percentage of kentucy blue grass TF = percentage of the other grass TF + K = 100% which is really 1.0 TF = 1 - K Now let's put them into the equation: (K times $5.75) + (TF times $4.50) = 5.75 now substitute so we only end up with one letter combo (K times $5.75) + (1 - K times 4.50) = 5.75 now multiply at this point I somehow make a mistake but can't find it below: (5.75K) + (4.50 X 1-k)= 5.75 5.75k + (4.5 - 4.5K) = 5.75 now simplify 10.25K + 4.5 = 5.75 subtract 4.5 from each side 10.25K = 1.25 but that turns out wrong. Hope that gets you started.