SOLUTION: Shomika was helping her family pick oranges. She took some oranges home to share with three friends. She gave three more than half to Jennifer. Angela got half of the remainder and

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Question 851436: Shomika was helping her family pick oranges. She took some oranges home to share with three friends. She gave three more than half to Jennifer. Angela got half of the remainder and three more. She gave Josie half of the remainder plus three. When she got home, she only had 10 left. How many did she have when she left the grove?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number she had when she left grove
She gave +x%2F2+%2B+3+ to jennifer, so she had
+x+-+%28+x%2F2+%2B+3+%29+ left
------------------------
She gave +%281%2F2%29%2A%28+x+-+x%2F2+-+3+%29+%2B+3+
+%281%2F2%29%2Ax+-+%281%2F4%29%2Ax+-+3%2F2+%2B+3+
+%281%2F4%29%2Ax+%2B+3%2F2+ to Angela, so she has left:
+x%2F2+-+3+-+%28+%281%2F4%29%2Ax+%2B+3%2F2+%29+
+x%2F2+-+3+-+%281%2F4%29%2Ax+-+3%2F2+
+%281%2F4%29%2Ax+-+9%2F2+
---------------------
She gave +%281%2F2%29%2A%28+%281%2F4%29%2Ax+-+9%2F2+%29+%2B+3+
+%281%2F8%29%2Ax+-+9%2F4+%2B+3+
+%281%2F8%29%2Ax+%2B+3%2F4+ to Josie, so she has left:
+%281%2F4%29%2Ax+-+9%2F2+-+%281%2F8%29%2Ax+-+3%2F4+
+%281%2F8%29%2Ax+-+21%2F4+
--------------------
+%281%2F8%29%2Ax+-+21%2F4+=+10+
+x+-+42+=+80+
+x+=+122+
---------------
She had 122 oranges when she left grove
check:
She gave +122%2F2+%2B+3+=+64+ to jennifer, so she had
+122+-+64+=+58+ left
She gave +58%2F2+%2B+3+=+32+ to Angela, so she had
+58+-+32+=+26+ left
She gave +26%2F2+%2B+3+=+16+ to Josie, so she had
+26+-+16+=+10+ left
as she should