### Author Topic: I need help on a question  (Read 3818 times)

#### wxc0212

• 2012 AMC Summer Group
• Mathcounts Chapter Champion
• • Posts: 17 ##### I need help on a question
« on: February 10, 2011, 10:26:01 PM »
While doing some practice questions my mom printed out for me i ran accross a question that i wasn't able to figure out.
Here's the question:

A positive number has a decimal part and an integer part. The decimal part, the integer part, and the positive number itself form a geometric sequence. Find this positive number.

#### yongcheng3315

• USAMO Winner
•     • Posts: 2585 ##### Re: I need help on a question
« Reply #1 on: February 11, 2011, 08:44:54 AM »
It is a hard problem. There are some hints in the answer key page for this problem.

Let a be the integer part of the number and b be the decimal part. The number can then be written as a + b.

Since the three terms of b, a, and a+b form a geometric sequence, the following equation is true:  a^2 = b(b+a).

Dividing both sides of the equation by a^2 you will get another equation.

Following the steps as shown in page 8 of the book, you will get the final result.

Good luck!