A landscaping company sells two types of grass a premium that sells for $1.25 per pound and standard mix for 0.95 per pound

Question

If the store manager dumps a 20-Ib bag of each mix into a large barrel what is the total value of the grass see in the barrel?

At what price per pound should the company sell this new mix to produce the same income as selling the two mixes separately?

if the store manager started with 20-In of the premium mix in a large barrel how many pounds of the standard mix should be added to create a mix that could be sold for $1.00 per pound?

how many pounds of grass seed must the barrel hold in order to contain all the mixture created in question 11?

how many pounds of the standard mix should be put in the barrel with 20Ib of the premium mix to create a mix with $1.10 per pound?

Answer 1

Premium grass seed sells for $1.25 per pound

Standard grass seed sells for $0.95 per pound

If the store manager dumps a 20-Ib bag of each mix into a large barrel what is the total value of the grass see in the barrel?

20 lb * P + 20 lb * S = 20 lb * $1.25 / lb + 20 lb * $0.95 / lb = $25 + $19 = $44 (note the units and how lb cancels 1/lb)

At what price per pound should the company sell this new mix to produce the same income as selling the two mixes separately?

Total weight is 2*20 lb = 40 lb. What we want is $/lb, so we need to divide total price to the total weight:

M = $44 / 40 lb = $1.10 / lb

if the store manager started with 20-In of the premium mix in a large barrel how many pounds of the standard mix should be added to create a mix that could be sold for $1.00 per pound?

We have 20 lb of P at $1.25 / lb. We need x lb of S at $0.95 / lb. Total price is

20 lb * $1.25 + x lb * $0.95

Total weight is 20 lb + X lb

We want per lb price to be $1.00

$1.00 = (20 * 1.25 + x * 0.95) / (20 + x) (multiply both sides with 20+x )

20 + x = 25 + 0.95x (subtract 0.95 from both sides)

20 + x - 0.95x = 25 (subtract 20 from both sides)

0.05x = 5 (divide both sides by 0.05 or multiply both sides with 20)

x = 100 lb

Answer 2

Hello, Samantha.

Okay, so the premium sells for $1.25/ pound

the standard sells for $ 0.95/ pound..

If the manager dumps 20 pounds of each mix into a barrel, then the value is:

1.25(20) + .95(20) =

25 + 19 = 44

So it costs $44 for 40 pounds.

To produce the same income as selling them separately, he would need to sell the new mix for

$ 44.00 ÷ 40 pounds = $1.10 / pound

To create a mix for $1.00/ pound:

He would mix 20 pounds of the premium with some amount of the standard mix. To find that amount

you would solve:

20(1.25) + x(.95) = 1.00(20 + x)

25 + .95x = 20 + x

25 - 20 = x - .95x

5 = .05x

x = 5/.05 = 100

He would need to mix 20 pounds of Premium with 100 pounds of Standard mix.