Question 1164359
<br>
Another tutor has shown a solution by the standard algebraic method.  It is a method you should know and be able to use, as it is applicable to a wide range of similar two-part "mixture" problems.<br>
If speed of finding an answer is important (as in a timed math competition) and formal algebra is not required, here is a quick way to answer any question like this with logical reasoning and some mental arithmetic.<br>
(The mental arithmetic in this example might be a stretch for many students; but the path to the final answer will still be faster than with formal algebra.)<br>
Consider the three per-pound prices on a number line: 3.30, 5.89, and 7.00.<br>
The price of the mixture is 259/370 = 7/10 of the way from 3.30 to 7.00.  (3.30 to 7.00 is a difference of 3.70; 3.30 to 5.89 is a difference of 2.59.  2.59/3.70 = 259/370 = 7/10.)<br>
That means 7/10 of the mixture is the more expensive coffee.<br>
ANSWER: 7/10 of 25 pounds, or 17.5 pounds, of the more expensive coffee; the other 7.5 pounds of the less expensive.<br>
CHECK:
17.5(7.00)+7.5(3.30) = 122.5+24.75 = 147.25
25(5.89) = 147.25<br>