<PRE><B>Question 1099310</B>
peter was given a crate of cups.
he sold all the cups.
each cup was sold for $8.90.
for every set of 5 cups sold a cup was given free.
 2/3 of the cups were sold in sets of 5 cups.
 He collected $1174.80.
 how many cups were in the crate at first.
:
let x = original number of cups
2/3 of the cups were sold as a set of 5 one free, therefore
5 * 8.90 = 44.50. They got 6 cups for 44.50 therefore
44.50/6 = 7.42 per cup
8.90*{{{1/3}}}x + 7.42*{{{2/3}}}x = 1174.40
multiply equation by 3
8.90x + 7.4167(2x) = 3523.20
8.90x + 14.733x = 3523.20
23.633x = 3523.20
x = 3523.20/23.633
x = 149.1 
We know it has to be an integer and a multiple of 3, lets assume
x = 150 cups originally
:
Find how many cups were paid for 
1174.4/8.90 = 132 cups, therefore
150-132 = 18 cups were free</PRE>