The Coffee Counter charges $8 per pound for Kenyan French Roast coffee and $7 per pound for Sumatran coffee. How much of each type should be used to make a 20 pound blend that sells for $7.30 per pound?

The price of the  Kenyan French Roast coffee is $6 and the price of Sumatran coffee is $14.

Two equations can be derived from the question:

8x + 7y = 20(7.3)

8x + 7y = 146 equation 1

x + y = 20 equation 2

Where: x

x = Kenyan French Roast coffee

y = Sumatran coffee.

To determine the value of y, multiply equation 2 by 8

8x + 8y = 160 equation 3

Subtract equation 1 from 3

y = 14

Substitute for y in equation 2

x + 14 = 20

x = 20 - 14

x = 6

To learn more about simultaneous equations, please check: link

Kenyan French Roast coffee x=6

Sumatran coffee y=14

Step-by-step explanation:

x+y=20     blend coffee

8x+7y=7.3(20)     selling price

x+y=20 ⇒ x=20-y

substitute in the equation:

8x+7y=7.3(20)

8(20-y)+7y=7.3(20) for 20 pound blend

160-8y+7y=146

-y=146-160

y=14 pond

x+y=20

x=20-14=6

check : 14*7+6(8)=146/7.3=20 pound

you save $70

discount would be 35% off

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.