## Tuesday, April 10, 2012

### at the TEF blog

This week's MGRE Math Beast Challenge problem, plus my attempted solution.

_

Dave said...

(Ed McMahon voice): You are correct, sir.

(sorry if I am posting twice, not sure which place I should respond to)

Lower tax percentage of 15%:
.15 time X = 8700
X = 8700 / .15
X = 58,000

Upper tax percentage of 35%:
.35 times X = 8700
X = 8700 / .35
X = 24,857.14

Both amounts are higher than the exclusion range, so you add the total amount of the range to both the upper and lower tax rates:
9800 - 5200 = 4600

58,000 + 4,600 = 62,600
24,857.14 + 4,600 = 29,457,14

All choices between these amounts, inclusive, are possible income amounts that yield an \$8,700 tax liability.

That would be the ones you identified in your solution.

Dave

Dave said...

OOps, I reviewed more carefully, and the \$63,500 answer does not appear to fall into the solution range. I think the only answers are \$33,200, \$43,300, and \$53,400.
I have fired my proof reader.
Dave

Kevin Kim said...

Interesting and plausible. But--

Lower tax percentage of 15%:
.15 time X = 8700
X = 8700 / .15
X = 58,000

Doesn't the exclusion need to be applied before you multiply by 0.15? I don't think you can apply the tax rate directly to unadjusted income. If you calculate the adjustment after you calculate the taxable income this way, you get a skewed figure-- or so it seems to me. Applying the exclusion rate retroactively doesn't correct for this skewing.

Same goes for:

Upper tax percentage of 35%:
.35 times X = 8700
X = 8700 / .35
X = 24,857.14

Here, too, X needs to be an adjusted figure before you try calculating income. Or am I smoking something, here? Maybe I'm just not following the logic.

Dave said...

Ok, totally started over, and I am going to work this a little at a time. Right now before I start, I am not sure where this is going.

The problem says the income tax rates are assessed 'after' the exclusion amount has been subtracted from his income. I read this as meaning that the percentage is not applied until the range of values have been subtracted from his true income.
The range of values is from 5200 to 9800.
This has two impacts on the problem.
1) If you make somewhere between 5200 and 9800, you are only taxed for 5199.
2) 5199 times 15 percent is nowhere near 8700; he will make far more than 9800 then.

The exclusion values now have only the meaning of an amount that is subtracted from his true income.

So, subtracting the exclusion range from his income means he subtracts 4600 from his income.
****NOTE: this may be the error if I am making one ****

8700 = .15 times (his real income - 4600)
8700 = .15 times (X - 4600)
8700 / .15 = X - 4600
58000 = X - 4600.
62,600 = X

If the exclusion range had not existed, then he would have been simply taxed at 15 percent of 62,600.
.15 times 62600 = 9390, which is way more than 8700.

This solution, if it is indeed one, requires that the way they calculate things is to subtract 4600 from his true income, which as far as I can see is what the problem says. But I could certainly be missing something.

Now I need an aspirin because my head hurts, lol...
Dave