# Problem of the Day: 1/26/13

A jar contains 4 red marbles & 4 blue marbles. If Shruti removes one marble at a time without replacement, what is the probability that the first 2 marbles she chooses are red?

Solution to yesterday’s problem:

Let’s designate the width of the photograph as x. Then the length of the photograph is x + 2. Since there is a 2-inch border on all sides of the photo, the width of the frame must be x + 4, and the length must be x + 2 + 4, or x + 6. We are given the fact that the area of the total frame is 120 square inches, so we can write an equation like this:

$(x+4)(x+6)=120$

This looks like a factored quadratic equation, but it isn’t because we need zero on the right side. So let’s turn it into a normal quadratic by FOILing (first, outer, inner, last):

$x^2+6x+4x+24=120$ or $x^2+10x+24=120$

Now to get zero on the right, all we have to do is subtract 120.

$x^2+10x-96=0$

To factor this, we need to find two factors of 96 whose difference is 10. We arrive at 6 and 16. So the factored form of this equation is

$(x+16)(x-6)=0$

This equation is true whenever either of the factors is zero; if x – 6 = 0 or if x + 16 = 0. Solving these two equations gives us x = 6 or x = -16. Obviously the width of the photo cannot be negative, so we know that the width is 6 inches.