Geometry Problems, Math Problems

Problem of the Day: 2/7/13

A square of side length 6 inches is inscribed in a circle. What is the radius of the circle? Express your answer in simplest radical form.

Solution to yesterday’s problem:

We can represent this problem using a pretty simple equation:

\frac{\textup{amt. of salt}}{\textup{total solution}}=\frac{7}{100}

The original solution was 500 mL of a 20% solution. This means that 20%, or 100 mL, was salt. Let’s put those in our equation:


Of course, this doesn’t work because we are adding 5% solution. Let’s call the amount of solution we’re adding x. Then our equation becomes


Solving this equation by cross-multiplying,





So you need to add 3250 mL, or 3.25 L, of 5% solution to get a 7% solution.


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