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Waiter A's compensation for any week is $500 plus 15 percent

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Waiter A's compensation for any week is $500 plus 15 percent [#permalink] New post 10 Aug 2018, 06:29
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Waiter A's compensation for any week is $500 plus 15 percent of the portion of A's total receipts above $600 for that week. Waiter B's compensation for any week is 25 percent of B's total receipts for that week. For what amount of total weekly receipts would both waiters earn the same compensation?



A.$12,200

B.$10,600

C. $8,900

D. $6,300

E. $4,100

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[Reveal] Spoiler: OA

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Re: Waiter A's compensation for any week is $500 plus 15 percent [#permalink] New post 10 Aug 2018, 10:01
For this question it is possible to do it by the tried and true method of attempting option D and B in that order, or by solving and equation. In both cases, it is easiest if you set up two functions first.

We know that waiter B earns 25% of their receipts, or 0.25x.

Waiter A earns 15% of their receipts after the first 600 dollars, with a starting wage of $500. So a function of their wage is then 500 + 0.15(x-600). This will give a wonky result if waiter A and waiter B earn the same amount for receipts less than $600, but as 0.25*600 = 150, this isn't the case.

Then we set up the equation:

0.25x = 500 + 0.15(x-600)

0.25x - 0.15x = 500-90

0.1x = 410

x = 4100

E

Alternatively, we know that waiter A originally earns more, so if an amount yields more money for waiter B, the actual amount must be lower. We can then check the results starting with the second lowest amount (D) (alternatively the second highest amount, personal preference).

0.25x for x = 6300 gives waiter B $1575

500 + 0.15(x-600) for x = 6300 gives waiter A $1355.

Waiter B receives more money, so the actual amount must be lower. The only lower amount is E, so we pick E.
Re: Waiter A's compensation for any week is $500 plus 15 percent   [#permalink] 10 Aug 2018, 10:01
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Waiter A's compensation for any week is $500 plus 15 percent

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