Question 1161205
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Here is a typical traditional algebraic setup for solving the problem.<br>
x pounds of coffee worth $50 per pound, plus 70 pounds of coffee worth $80 per pound, equals (70+x) pounds of coffee worth $70 per pound:<br>
{{{50(x)+80(70) = 70(70+x)}}}<br>
The equation is easily solved using basic algebra.<br>
Here is an alternative method that can be used if a formal algebraic solution is not required.  For this particular problem, the amount of work required for both methods is comparable; but for many mixture problems like this, this alternative method can be MUCH faster and easier.<br>
The per-pound price of the mixture ($70) is 2/3 of the way from the per-pound price of the lower priced coffee ($50) to the per-pound price of the higher priced coffee ($80).<br>
That means 2/3 of the mixture must be the higher priced coffee.  In other words, the more expensive coffee and the less expensive coffee should be mixed in the ratio 2:1.<br>
Since she is using 70 pounds of the more expensive coffee, she should use half as much -- 35 pounds -- of the less expensive coffee.<br>
Of course that is the answer you should get using the formal algebraic method shown above.<br>