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:

\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.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s