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question from Grockit - can't get it

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by wiut » Mon Jan 10, 2011 3:57 am
Ann and Bill are both salespeople at a car dealership. Ann earns $1250 each month plus 0.4 percent of her sales over $200,000 for that month. Bill earns 0.5 percent of his total sales each month. If in a given month Ann and Bill earned the same amount of money and had the same total sales, what was each of their total sales for that month?


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by sanju09 » Mon Jan 10, 2011 4:12 am
wiut wrote:Ann and Bill are both salespeople at a car dealership. Ann earns $1250 each month plus 0.4 percent of her sales over $200,000 for that month. Bill earns 0.5 percent of his total sales each month. If in a given month Ann and Bill earned the same amount of money and had the same total sales, what was each of their total sales for that month?


Thank you!

If $t was each of their total sales for that month, then Ann's earnings in the month

= $[1250 + 0.004 (t - 200000)], and that of Bill's

=$0.005 t

Since, the two earnings are given as equal, we can have

$[1250 + 0.004 (t - 200000)] = $0.005 t

0.005 t - 0.004 t = 1250 - 800

0.001 t = 450

Or t = [spoiler]$450,000[/spoiler]
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by GMATGuruNY » Mon Jan 10, 2011 4:13 am
wiut wrote:Ann and Bill are both salespeople at a car dealership. Ann earns $1250 each month plus 0.4 percent of her sales over $200,000 for that month. Bill earns 0.5 percent of his total sales each month. If in a given month Ann and Bill earned the same amount of money and had the same total sales, what was each of their total sales for that month?

Thank you!
We could plug in the answer choices, one of which would say that Ann and Bill each had sales of $450,000.

Answer choice: $450,000 sales for each
Ann's sales over 200,000 = 450,000 - 200,000 = 250,000.
Ann earns = 1250 + .004*250,000 = 1250+1000 = 2250.
Bill earns = .005*450,000 = 2250.
Success! Ann and Bill earn the same amount.
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by frank1 » Mon Jan 10, 2011 4:13 am
wiut wrote:Ann and Bill are both salespeople at a car dealership. Ann earns $1250 each month plus 0.4 percent of her sales over $200,000 for that month. Bill earns 0.5 percent of his total sales each month. If in a given month Ann and Bill earned the same amount of money and had the same total sales, what was each of their total sales for that month?


Thank you!
Lets sales be X
same for both as per question
now
1250+(X-200,00)x.(04/100)=(0.5/100)*X

i think this gives value for X

If it were gmat question best tactics would be to backsolve and check options in this equation
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by wiut » Mon Jan 10, 2011 4:27 am
First of all, thanks to the Experts (and non-experts) for such a fast reply! Its fantastic! I never actually thought that it could be that fast! :!:

The explanation is perfect! Actually, I just made an error with (t-200,000) - I used (200,000*0,004x).

Once again, many thanks and good working week for everyone! :!: :!: :!:
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