Question 1201904
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I would strongly recommend against using the "magic" formula that tutor @josgarithmetic likes to show whenever they respond to a mixture problem like this.  Blindly using the formula does not teach the student anything about how to solve the problem; and it is an ugly formula that is both hard to learn and hard to use correctly.<br>
For a typical formal algebraic solution, look at the response from the other tutor.<br>
And if formal algebra is not required, here is a quick and easy informal (and easy to understand) way to solve any 2-part mixture problem like this.<br>
(1) Using a number line (if it helps), determine that the $6.75 cost per pound of the mixture is 5/6 of the way from $5.50 to $7.00.<br>
(2) That means 5/6 of the mixture is the more expensive coffee beans.<br>
Then use simple arithmetic to determine that 5/6 of 4.5 pounds is 3.75 pounds, so...<br>
ANSWER: 3.75 pounds of the light roast coffee; 0.75 pounds of the dark roast.<br>