Question

Three varieties of coffee Coffee​ A, Coffee​ B, and Coffee C are combined and​ roasted, yielding a 55​-lb batch of coffee beans. Twice as many pounds of Coffee​ C, which retails for ​$10.39 per​ lb, are needed as Coffee​ A, which sells for ​$14.99 per lb. Coffee B retails for ​$13.99 per lb. How many pounds of each coffee should be used in a blend that sells for ​$12.61 per​ lb?

Answer 1

Coffee A is 12.241 pounds, Coffee B is 18.269 pounds and Coffee C is 24.482 pounds.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let a pounds of coffee A needed

Let b pounds of coffee B needed

Let c pounds of coffee C needed

c= 2a.................(1)

a+ b+c= 55..........(2)

and, 14.99 a+ 13.99 b + 10.39 c /55 = 12.61

1499a + 1399 b + 1039 c = 69,355...............(3)

Subtract (2) from (3), we get

  1499 a+ 1399 b + 1039 c= 69355

-  1039 a - 1039 b - 1039 c = 57145

_____________________________

  460 a + 360 b = 12210

 46a+ 36 b = 1221

b= 1221/ 36 - 46 a/ 36

b= 407 / 12 - 23 a / 18

Put b in Equation (2)

a + 407 / 12 - 23 a / 18 + 2a= 55

-5a / 18 + 2a + 407/ 12 = 55

31a/ 18 = 253/ 12

a= 4554 / 372

a = 2277/ 186

a= 759/ 62

a= 12.241

and, c=2a = 24.482

b= 33.91 - 15.641

b= 18.269

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