Question 1202720
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For a standard formal algebraic solution, look at the response from tutor @ikleyn.<br>
If you like doing mathematics using "magical" formulas, thereby gaining absolutely no understanding of HOW the problem is actually solved, then look at the response from tutor @josgarthmetic.<br>
If formal algebra is not required, and you want a fast and easy way to solve the problem informally, then below are two closely related methods for solving any 2-part mixture problem like this.<br>
First method....<br>
(1) Look at the prices per pound of the two kinds of tea and the mixture -- on a number line, if it helps: $2.00, $2.50, and $5.00.
(2) Observe/calculate that $2.50 is 1/6 of the way from $2.00 to $5.00. ($2.00 to $5.00 is a difference of $3.00; $2.00 to $2.50 is a difference of $0.50; $0.50/$3.00 = 1/6.)
(3) That means 1/6 of the mixture is the more expensive Earl Grey tea.<br>
1/6 of 300 pounds is 50 pounds.<br>
ANSWER: 50 pounds of Earl Grey tea and 300-50 = 250 pounds of Orange Pekoe tea<br>
Second method....<br>
(1) Again look at the prices per pound of the two kinds of tea and the mixture.
(2) The difference between the prices of the Orange Pekoe tea and the mixture is $0.50; the difference between the prices of the Earl Grey tea and the mixture is $2.50.  The ratio of those two differences is $0.50:$2.50 = 1:5.
(3) Interpret that to mean that the $2.50 cost per pound of the mixture is "5 times as close" to $2.00 as it is to $5.00.
(4) That means the mixture must contain 5 times as much Orange Pekoe tea as Earl Grey tea.<br>
Use mental arithmetic (or formal algebra, if needed) to find that 300 pounds mixed in the ratio 5:1 means 250 pounds of Orange Pekoe tea and 50 pounds of Earl Grey tea.<br>
ANSWER (again, of course): 50 pounds of Earl Grey tea and 300-50 = 250 pounds of Orange Pekoe tea<br>