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Sarah gets \$4 for every watch she sells. She gets \$5 bonus for every 25 watches she sells.

How many watches did she sell last month if she made \$506?

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    From the given data, she sold $121.5$ watches. – 2017-01-26
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    So for every 25 watches sold, there is a profit of $4(25) + 5 = 105$ dollars (assuming I understand the question correctly). Does this help? – 2017-01-26

2 Answers 2

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Let $b=\left\lfloor\dfrac{506}{105}\right\rfloor$, the number of bonuses she got.

Then she sold

$$25\cdot b+\frac{506-105\cdot b}4$$ watches (?!).

The equation

$$4\cdot a+105\cdot b=506$$

has the only solution $a=74,b=2$ (taking the modulo $4$, we have $b\equiv 2$).

So either Sarah is rewarded only when she sells $25$ watches in a single go, which occurred twice (and she sold $124$ watches), or both her and her boss suffer from dyscalculia.

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For every 25 watches sold, there is a profit of $4(25) + 5 = 105$ dollars. So if Sarah sells 100 watches, she makes $4(105) = 420$ dollars. In order to make the additional 86 dollars, Sarah must sell at least 22 more watches. This will give a profit of $420 + 22(4) = 508$ dollars. (There is no possible way for her to make exactly 506 dollars).