If one factor of 56x^4-42x^2y6 is 14x^2y^3 what is the other factor?
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Let x be the amount of the 30% alcohol and let y be the amount of 5% alcohol.
We want the total amount to by 25 gal, then we have:
We also want the resulting mix to be 25% alcohol, this is 0.25 in decimal form; also we know that the first type of alcohol is 30% and the second is 5%, then we have:
Hence we have the system of equations:
To solve the system we solve the first equation for y:
then we plug this value of y in the second equation:
Once we have the value of x we plug it in the expression we found for y:
Therefore, the mixture will have 20 gallons of 30% alcohol and 5 gallons of 5% alcohol.