SOLUTION: Elliott went to the store for a bag of cookies. When he left the store he gave his mom half the cookies and half a cookie. He then came upon his aunt and gave her half the remainin

Algebra ->  Human-and-algebraic-language -> SOLUTION: Elliott went to the store for a bag of cookies. When he left the store he gave his mom half the cookies and half a cookie. He then came upon his aunt and gave her half the remainin      Log On


   

Question 648743: Elliott went to the store for a bag of cookies. When he left the store he gave his mom half the cookies and half a cookie. He then came upon his aunt and gave her half the remaining cookies and half a cookie. Continuing on his way, he found his friend and gave him half the cookies left and half a cookie. When made it to class, he only had six cookies left. How many did he start out with?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = number of cookies he started with
After giving some to Mom, he has left
+c+-+c%2F2+-+1%2F2++=+c%2F2+-+1%2F2+
After giving some to Aunt, he has left
+c%2F2+-+1%2F2+-+%28+c%2F4+-+1%2F4+%29+-+1%2F2+=+c%2F4+-+3%2F4+
After giving some to a friend he has left
+c%2F4+-+3%2F4+-+%281%2F2%29%2A%28+c%2F4+-+3%2F4+%29+-+1%2F2++=+c%2F8+-+7%2F8+
He ends up with 6 cookies, so
+c%2F8+-+7%2F8+=+6+
+c+-+7+=+48+
+c+=+55+
He started with 55 cookies
check answer:
He gave Mom +55%2F2+%2B+1%2F2+=+56%2F2+
+56%2F2+=+28+,
so he has left +55+-+28+=+27+
He gave Aunt +27%2F2+%2B+1%2F2+=+28%2F2+
+28%2F2+=+14+,
so, he has left +27+-+14+=+13+
He gave friend +13%2F2+%2B+1%2F2+=+14%2F2+
+14%2F2+=+7+
He has left +13+-+7+=+6+
OK