book Maths Puzzle Numerical Ability

How much water should be added to 30 gallons of a solution that is 70% antifreeze in order to get a mixture that is 60% antifreeze?

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Can you please explain to me what an algebraic proof is? I know you give a statement such as: all alternate interior angles are congruent. But how would you prove the statement? This is called a Literal Equation.
Solve (x+7)(y+4)=5 for x in the form x=ay+b/y+c