Question 1183227
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Here is an alternative method for solving 2-part mixture problems like this, if a formal algebraic solution is not required.<br>
You are mixing 10% ethanol and 85% ethanol, and you want to get 25% ethanol.
Look at the three percentages on a number line and observe/calculate that 25% is 1/5 of the way from 10% to 85%.  (10 to 85 is a difference of 75; 10 to 25 is a difference of 15; 15/75 = 1/5.)
That means 1/5 of the mixture needs to be the higher percentage ingredient.<br>
ANSWER: 1/5 of 10 gallons, or 2 gallons, of the 85% ethanol; the other 8 gallons of 10% ethanol.<br>
CHECK:
.85(2)+.10(8) = 1.7+.8 = 2.5
.25(10) = 2.5<br>