Challenging rational expression question that includes probability

Question

This is the question: Consider an experiment in which a marble is tossed into a box whose base is shown in the figure. The probability that the marble will come to rest in the shaded portion of the box is equal to the ratio of the shaded area to the total area of the figure. If the probability is equal to 3/10, find the positive value of x. 

First, large box (rectangle): on the right side it is 2x+1, and on the bottom it is 3x+2.

Second box (rectangle), inside the first one: right side is x+1, bottom is x+2.

It also mentions that the area of a rectangle is bh.

Answer 1

The equation you are likely expected to set up:

(x+1)(x+2) 3

------------------ = ----------

(2x+1)(3x+2) 10

where the numerator on the left represents the area of the shaded region and the denominator the area of the entire base of the box. Multiply the binomials, cross-multiply and use standard techniques for solving a quadratic equation.

Something like:

8x^2 -9x -14 = 0 (which can be solved by factoring).