# 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:

$\frac{100}{500}=\frac{7}{100}$

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

$\frac{100+0.05x}{500+x}=\frac{7}{100}$

Solving this equation by cross-multiplying,

$100(100+0.05x)=7(500+x)$

$10000+5x=3500+7x$

$6500=2x$

$x=3250$

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