Ms. Morris invested in Fund A and Fund B. The total amount he invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Ms. Morris invest in Fund A? Pick one:
A) $32,000 B) $36,000 C) $40,000 D) $42,000 E) $45,000
solution   This one could be solved with a good deal of hairy algebra, but backsolving is an incredibly efficient alternative. Let’s start with (C) — we’ll say Ms. Morris invested $40,000 in Fund A, which means she invested $60,0000 in fund B. In Fund A, she earned 23%, which was   (0.23)*40000= 
<gadget id="calculator">  (0.23)*40000</gadget>
<output>9_200</output>
$9200. In Fund B, she earned 17%, which was   (0.17)*60000= 
<gadget id="calculator">  (0.17)*60000</gadget>
<output>10_200</output>
$10200. Here, the interest earned in Fund B was $1000 more than the interest earned in Fund A, a bigger difference than we want. To make the difference smaller, we need less money in Fund B and more money in Fund A. Eliminate answers (A) &amp; (B) &amp; (C). Try D: We’ll say Ms. Morris invested $42,000 in Fund A, which means she invested $58,000 in Fund B. In Fund A, she earned 23%, which was   (0.23)*42000= 
<gadget id="calculator">  (0.23)*42000</gadget>
<output>9_660</output>
$9660. In Fund B, she earned 17%, which was   (0.17)*58000= 
<gadget id="calculator">  (0.17)*58000</gadget>
<output>9_860</output>
$9860. The difference is exactly $200, so answer $42,000
<result>D</result>
Ms. Morris invested in Fund A and Fund B. The total amount he invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Ms. Morris invest in Fund A?