Ok so I'm reviewing algebra since it was the only math class I didn't do well in and thought I would work out all the problems in the Schaum's Outline. I have ran across 3 problems I'm not sure how to do.

a)Two numbers have the ratio 3:4. If 4 is added to each of the numbers the resluting ratio is 4:5. Find the two numbers.

b) Determine whether the graph of each relation is symmetric with respect to the y axis, x axis, or origin.

$\displaystyle y = (x-3)^3$

I want to work this one out rather than look at the graph.

$\displaystyle y = (x-3)^3$

$\displaystyle -y= (-x-3)^3$

$\displaystyle (-x-3)^3 = (-x)^3 -3(-x)^2(-3) +3(-x)(-3)^2 -(-3)^3$

$\displaystyle (-x-3)^3 = -x^3 + 9x^2 -27x +27$

$\displaystyle -y= -x^3 + 9x^2 -27x +27$

$\displaystyle y = x^3 - 9x^2 + 27x -27$

So it is symmetric with respect to the origin but is there a faster way of showing that. I tried going this route but got stuck

$\displaystyle -y = (-x-3)^3$

$\displaystyle -y = (-1)^3(x+3)^3$

and then got stuck.

c)Find the largest rectangle which can be inscribed in a right triangle whose legs are 6 and 8 inches repectively.

I know $\displaystyle A= xy$

and

$\displaystyle x^2 + y^2 = 100$

Thanks in advance