A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 4 for 85 cents. How many were sold at the first rate?	Choose the correct choice from the following choices.
A) 45
B) 21
C) 9
D) 16
E) 13
This can be solved like a classical mixture problem but numbers are awkward to deal with.   It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 4.   100 - 45 = 255 =&gt; not a multiple of 4 so exclude   100 - 21 = 279 =&gt; not a multiple of 4 so exclude   100 -9 = 291 =&gt; not a multiple of 4 so exclude   100 - 16 = 284 =&gt; a multiple of 4 so keep   100 - 13 = 287 =&gt; not a multiple of 4 so exclude   Hence, answer choice 16 is correct.   16
<result>D</result>
A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 4 for 85 cents. How many were sold at the first rate?