How many pounds in regular coffee ( selling $4 per pound) and how many pounds of kona coffee (selling $11.50 per pound) must be combined to get 20 pounds of a mixture worth $6 per pound? be sure to write a system of two equations in two variables to solve the proplem.

Selling price of regular coffee = $4 per pound

Selling price of kona coffee = $11.5 per pound

Total mixture required = 20 pounds

Selling price of mixture = $6 per pound

Let quantity of regular coffee be 'a' and that of kona coffee be 'b'

⇒ Total mixture required = a + b

⇒ 20 = a + b ..................... (i)

Selling price of one pound of mixture = Price of total mixture ÷ Total pounds of mixture

⇒ 6 = [(4*a) + (11.5*b)] ÷ (a+b)

⇒ 6*a + 6*b = 4*a + 11.5*b

⇒ 2a = 5.5b

⇒ 20a = 55b

⇒ 4a = 11b

⇒ a = b ....................... (ii)

Substituting the value of (ii) in (i)

b + b = 20

⇒ 11b + 4b = 20 * 4

⇒ 15b = 80

⇒ 3b = 16

⇒ b =

and a = *

⇒ a =

So, to make the mixture we would require of regular coffee and of kona coffee.

i believe the correct answer is b.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have