Question

a nursery sells kentucky bluegrass 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 nusery uses in in 5 pounds of the mixture

Answer 1

Answer:

$k=3$

Step-by-step explanation:

Given that:

Per pound cost of kentucky bluegrass seed = $5.75

Per pound cost of tall fescue seed = $4.50

Per pound cost of mixture of seeds = $5.25

$k$ is the amount of kentucky blue grass.

Total amount of the mixture = 5 pounds

Therefore, amount of tall fescue seed = (5 - $k$) pounds

To find:

The value of $k$.

Cost of $k$ pounds of kentucky bluegrass seed = $\ 5.75k$

Cost of (5 - $k$) pounds of tall fescue seed = $\ (5-k)4.50$

As per question statement:

$5.75k+(5-k)4.50=5.25\times 5\\\Rightarrow 575k+5\times 450 -450k=525\times5\\\Rightarrow 125k=75\times5\\\Rightarrow k =3\ pounds$

Amount of kentucky blue grass seed used = 3 pounds

Amount of tall fescue seed used = 5-3 = 2 pounds