Answer
A binder costs 2.29, a ream of paper costs 4.29, and a notebook costs .79 dollars.
Work Step by Step
We first set up three equations, using z as the cost of a ream of paper, y as the cost of a notebook, and x as the cost of a binder.
$3x + z + 4y = 14.32 \\ x + 2z + 5y = 14.82 \\ 2x + 3y + 3z = 19.82$
In order to solve systems of three linear equations, we multiply the first and second equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by -2 and the second equation by 1 and add to obtain:
$-5x -3y = -13.82$
We now multiply the first and third equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by -3 and the third equation by one and add to obtain:
$ -7x -9y = -23.14 $
Plugging $x =-.6y +2.764$ into this equation, we obtain:
$-4.8y -19.348 = -23.14 \\ y =.79 $
Now, we plug this value into one of the equations that only has x and y in them to find:
$ x = 2.29$
Finally, we plug the values of x and y into the first equation listed in the book to find:
$ z = 4.29$
