Cynthia

Problem:

Cynthia must cut a 113.4 inch piece of piece into three pieces. The first piece must be half as long as the second piece and 11.2 inches longer than the third. How long each piece should be.

Solution:

Let $ x $, $ y $ and $ z $ be the lengths of the first, second and third piece respectively.

We have this condition:

The first piece must be half as long as the second piece, that becomes

$ x = \frac{y}{2} $, or simply $ 2x = y $.

Next, we also have this condition:

The first piece must be 11.2 inches longer than the third, that becomes

$ x = 11.2 + z $, in other words, $ z = x - 11.2 $

Or course, the three pieces add up to 113.4 inches, that means

$ x + y + z = 113.4 $.

The simplest way to solve this is to represent all these in terms of  $ x $

$ \begin{eqnarray*} x + 2x + (x - 11.2) &=& 113.4 \\ 4x - 11.2 &=& 113.4 \\ 4x &=& 124.6 \\ x &=& 31.15 \end{eqnarray*} $

Therefore we get the the first piece is 31.15 inches, the second piece should be $ 31.15 \times 2 = 62.3 $ inches, the last piece is $ 31.15 - 11.2 = 19.95 $ inches.