Math brain teaser to pick your brain

Dear Aunt Sally is now in her fifties, but is still working and putting away money for retirement. It is nearly the deadline for her to file her taxes, and she will have to pay. Right now, she owes $1,000. She has $2,000 cash on hand to use to pay it, but she can also put some of that money toward retirement. Every dollar she puts toward retirement will lower her taxes by about $0.25 If she wants to use the $2,000 for a combination of paying her tax and saving for retirement, how much should she pay to still pay her taxes completely, and also get the biggest break she can get on her taxes for this year? [Hint: Remember that as Aunt Sally puts money in retirement, her taxes will go down. Also, remember that she is not going to want to owe the IRS any money, so she cannot just put it all in retirement, for example.]

Let x = amount that Aunt Sally puts away toward retirement

For each dollar, taxes owed are lowered by $0.25
Total owed (after putting away x dollars toward retirement) = 1000 - 0.25x
Total amount left to pay for taxes (after putting away x dollars) = 2000 - x

1000 - 0.25x = 2000 - x
x - 0.25x = 2000 - 1000
0.75 x = 1000
x = 1000/0.75
x = 1333.33

--------------------

Dear Aunt Sally should put away $1,333.33 toward retirement

This leaves her with $2,000 - $1,333.33 = $666.67

Her taxes get reduced by 0.25 * $1,333.33 = 333.33

Taxes owed are now $1,000 - $333.33 = $666.67

So Aunt Sally has just enough money to pay her taxes!

let x be the money paid off directly as taxes
let y be the money invested for retirement.

x + y = 2000
x + 0.25y = 1000
--------------------------
0.75y = 1000
y = $1,333.33

x + y = 2000
x + .25y = 1000
x = 2000 - y
2000 - y + .25y = 1000
1000 = .75y
y = 4000/3 dollars in savings
x = 2000/3 dollars on taxes

tax=1000-ret*0.25
tax+ret=2000

so that

tax = 667
ret = 333