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:

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):

or

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

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

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*.

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