Question

Please explain how to solve this problem

Answer 1

9514 1404 393

Answer:

• 100 pounds Earl Grey
• 300 pounds Orange Pekoe

Step-by-step explanation:

Let x represent the number of pounds of Earl Gray tea in the mix. Then the total cost of the mix is ...

  6x +4(400-x)=4.50(400)

  2x +1600 = 1800 . . . . . . . simplify

  2x = 200 . . . . . . . . . . . subtract 1600

  x = 100 . . . . . . . . . . . divide by 2. Pounds of Earl Grey

  (400 -x) = 300 . . . . . Pounds of Orange Pekoe

The blend should have 100 pounds of Earl Grey and 300 pounds of Orange Pekoe.

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Additional comment

It is easy to show that the relationship between the quantities of high-cost (H) and low-cost (L) items in the mix (M) is ...

  fraction of mix that is H is (M -L)/(H -L)

Here, we have H=6, L=4, M=4.5, so the fraction of the mix that is Earl Grey is ...

  (4.5 -4)/(6 -4) = 0.5/2 = 0.25

There are 400 pounds of mix, so 0.25(400) = 100 pounds is Earl Grey.

The solution above is essentially 2-step, so using this relation doesn't necessarily save any steps. It just makes it possible to solve the problem in your head.