<p>How many gallons of 40% alcohol solution must be nixed with 70% solution to obtain 30 gallons of a 52% alcohol solution?</p>
<p>where did u find this math problem?</p>
<p>.4x + .7x=30 x .52</p>
<p>1.1x=15.6</p>
<p>x=14.18</p>
<p>.4 x 14.18</p>
<p>= 5.672</p>
<p>i am completely wrong i bet, i have no idea... no solution????</p>
<p>is this an SAT problem? cause it seems odd to be on the SAT</p>
<p>.4x + .7y = 30 x .52
x + y = 30</p>
<p>x = 30 - y
.4(30-y) + .7y = 15.6
12 - .4y + .7y = 15.6
12 + .3y = 15.6
.3y = 3.6
y = 12 gallons</p>
<p>x + 12 = 30
x = 18 gallons</p>
<p>so...18 gallons of 40% alcohol and 12 gallons of 70% alcohol</p>
<p>why is x + y = 30? Where did .4 or .7 or .52 go?</p>
<p>I set up a system of two equations. The first uses the percentages of alcohol, while the second is the actual volume of the alcohol. You know that the combinations of 40% and 70% must equal 52% of 30 gallons, and you also know that the combinations of 40% and 70% must equal 30 gallons total.</p>
<p>.4, .7, and .52 are in the first equation.</p>
<p>you have 2 unknowns, the amount of 40% solution and the amount of 70% solution that you will combine to have a total of 30 gallons of 52% solution.
so the amount of 40% + the amount of 70% = 30 gallons
or x+y=30
now that we have a variable to describe how many gallons of each will be added, we can put
.4x + .7y= .52(30)
this ensures that you will have a 52% solution at the end.</p>
<p>52 - 40 = 12,
70 - 52 = 18.
52 breaks the segment [40, 70] in the 12:18 ratio.</p>
<p>THE RULE:
Take solutions in the opposite ratio.</p>
<p>18 parts of 40% and 12 parts of 70% will make 52% concentration.</p>
<p>30 gallons breaks nicely into 18 and 12 gallons.</p>