Question 1163316
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You should understand the formal algebraic solution method shown by the other tutor; it is a good example of problem solving using algebra.<br>
However, if a formal algebraic solution is not required, you can get to the answer to any two-part mixture problem like this quickly and easily using logical reasoning and simple mental arithmetic.<br>
As noted in the response from the other tutor, it is going to take a lot of the 80% antifreeze to mix with the 30% antifreeze to get 70% antifreeze, because 70% is much closer to 80% than it is to 30%.<br>
Putting numbers to that general concept, the ratio of the amounts of the two ingredients is exactly dependent on where the 70% target lies between the 30% and 80% of the two ingredients.<br>
Simple mental calculation shows that 70% is 4/5 of the way from 30% to 80%.  (From 30 to 80 is a difference of 50; from 30 to 70 is a difference of 40; 40/50 = 4/5.)<br>
That means 4/5 of the mixture must be the 80% antifreeze.<br>
So the 70 gallons of 30% antifreeze is 1/5 of the mixture; that means the 4/5 of the mixture that is the 80% antifreeze is 4*70 = 280 gallons.<br>
ANSWER: 280 gallons of the 80% antifreeze are needed.<br>
CHECK:
.30(70)+.80(280) = 21+224 = 245
.70(70+280) = .70(350) = 245<br>