Question 1200059
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(1) A standard formal algebraic solution....<br>
x gallons of 0% antifreeze, plus 1 gallon of 100% antifreeze, yields (x+1) gallons of 85% antifreeze:
0(x)+1.00(1)=0.85(1+x)
1=.85+.85x
.85x=.15
x=.15/.85 = 15/85 = 3/17<br>
ANSWER: 3/17 gallons<br>
(2) One quick and easy alternative for an algebraic solution....<br>
1 gallon of 100% antifreeze; x gallons of water; the ratio of gallons of antifreeze to gallons of water is 1:x<br>
The ratio of antifreeze to water in the mixture is 85:15 = 17:3, so<br>
1/x = 17/3
17x = 3
x = 3/17<br>
ANSWER: 3/17 gallons<br>
(3) And a quick and easy informal solution method....<br>
85% is 85/100 = 17/20 of the way from 0% to 100%, so 17/20 of the mixture is the original 1 gallon of antifreeze.
That means 3/20 of the mixture is the added water; so the amount of water added is 3/17 of the amount of antifreeze. 3/17 of 1 gallon is 3/17 gallons, so<br>
ANSWER: 3/17 gallons<br>
Assuming the student is learning how to solve problems using formal algebra, you want to understand method (1) above.<br>
But if the speed of obtaining the answer is important and formal algebra is not required (as in a timed math competition), being able to use one of the other methods is to your advantage.<br>