SOLUTION: Without solving, explain what is wrong with the following mixture problem: How many gallons of 30% antifreeze should be added to 25 gallons of 40% antifreeze to obtain a solution

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Question 828194: Without solving, explain what is wrong with the following mixture problem: How many gallons of 30% antifreeze should be added to 25 gallons of 40% antifreeze to obtain a solution of 45% antifreeze? Now go through an algebraic solution. What happens?

Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!
The question incorrectly expects a resulting concentration outside the bounds of the two solution concentrations to be mixed. No sense in trying to solve the equation, but the equation would be this:

, just impossible for the situation; z is amount of the 30% to add.

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
You can't get a greater concentration of
antifreeze by mixing two lesser concentrations
----------------
Let = gallons of 30% antifreeze needed

You get a negative amount to be added
which makes no sense

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Without solving, explain what is wrong with the following mixture problem: How many gallons of 30% antifreeze should be added to 25 gallons of 40% antifreeze to obtain a solution of 45% antifreeze? Now go through an algebraic solution. What happens?

A 30% solution CANNOT be added to a 40% solution to obtain a 45% solution!!