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Expert: Robi Bhattacharjee - 3/20/2009


Question
I'm having trouble with 2 questions:
1. A margin x inches wide is drawn on a book cover measuring 12 in. by 14 in.  If the area of the margin is 88 inches squared. find x
2. A rectangular garden is 20m by 30m. A path of uniform width surreounds the garden. If the total area of the garden and the path is 936m squared, how wide is the path?

Answer
Hi Ann,

I will set up the equations for both problems. As an exercise, you should solve those equations. So here goes.

1. The dimensions of the cover excluding the margin will be 12 - 2x by 14 - 2x. This is easy to see if you draw a picture.

So the area of the cover NOT including the margin is (12 - 2x)(14 - 2x).

However, we also know that it is 12*14 - 88 = 80.

So (12 - 2x)(14 - 2x) = 80.



2. The new dimensions of the garden including a path x m wide are (20 + 2x) by (30 + 2x). Once again, a picture works wonders.

So (20 + 2x)(30 + 2x) = 936.


Have fun solving and good luck,
Robi

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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