SOLUTION: Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 2 feet larger than that of the small circle and the ratio of the circumference is 3:1,

Question 1003367: Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 2 feet larger than that of the small circle and the ratio of the circumference is 3:1, what are the radii of the two circles?
I know that the circumference is C=2"Pi"r but how am I solving this when the circumference is in ratio form and one ratio is 2 feet larger? I tried to figure it out with diameter (d=2*r) but I don't know the diameter either. I also tried referring to this guide(http://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.310984.html) as well since it was useful in a previous problem but not so with the above one.
Answer by ikleyn(52752) (Show Source): You can put this solution on YOUR website!
.
Let x = the radius of the smaller circle and
y = the radius of the larger circle.

Then you have

y = x + 2,

= 3.

In the last equation, reduce the ratio to the left by . You will get

= 3.

Now you have the system of 2 equations

.

Can you solve it?

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Comment from student: Thank you for your assistance but I'm still having a hard time trying to solve those problems.
There could be many things where y/x=3. I don't know how to solve for y=x+2 given only one number. I guess what is really
throwing me off is the circumference given in 3:1 ratio. I know that I could solve r= c/2PI but I can't solve 3:1/2pi.
I tried doing 3/2pi which gave me 0.477 but I don't think that is right.
---------------------------------------------------------------

OK, I will continue and will solve this system.

From its second equation y = 3x.
Substitute it into the first equation instead of y. You will get

3x = x + 2,

3x - x = 2,

2x = 2,

x = 1.

Answer. x = 1, y = 3.

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