While Joanne is gathering apples from her family’s orchard, her sister comes outside to help her. Joanne gathers 30 apples from the tallest trees, half this amount from the shortest trees, and more apples from the average trees. Compared with Joanne, her sister gathers twice as many apples from the tallest trees and 3 times as many apples from the shortest trees. She doesn't take any from the average trees. If the sisters have gathered a combined total of 500 apples, how many apples did Joanne gather from the average trees?
Joanna gathered 30 apples / 2 = 
<gadget id="calculator">30/2</gadget>
<output>15</output>
15 apples from the shortest trees.
Her sister gathered 30 apples * 2 = 
<gadget id="calculator">30*2</gadget>
<output>60</output>
60 apples from the tallest trees.
Her sister also gathered 15 apples * 3 = 
<gadget id="calculator">15*3</gadget>
<output>45</output>
45 apples from the shortest trees.
In total, her sister gathered 60 + 45 = 
<gadget id="calculator">60+45</gadget>
<output>105</output>
105 apples.
From the tallest and shortest trees, Joanna gathered 30 + 15 = 
<gadget id="calculator">30+15</gadget>
<output>45</output>
45 apples.
So far, the sisters have a combined total of 105 + 45 = 
<gadget id="calculator">105+45</gadget>
<output>150</output>
150 apples.
Therefore, Joanna must have gathered 500 total apples - 150 apples so far = 
<gadget id="calculator">500-150</gadget>
<output>350</output>
350 apples from the average trees.

<result>350</result>