Problema Solution
After The Football Game
A group of students went to their favorite restaurant after the football game one Friday night. They all ordered from the menu and forgot to tell the server to give them separate checks. The bill totaled $27, including the tip. They decided to split the bill evenly, and they figured out how much each of them owed. But then three people said they had no money. The rest of the people each had to chip in 45 cents extra to cover the tab. How many people were in the group?
Answer provided by our tutors
Let
x = the number of people in the group, x>0
a = the amount of money that each of them has to pay after the split, a>0
x*a = 27 => a = 27/x
But then three people said they had no money. The rest of the people each had to chip in 45 cents extra to cover the tab.
(x - 3)(a + 0.45) = 27 (since 45 cents = $0.45)
if we replace a = 27/x in the above equation we get
(x - 3)(27/x + 0.45) = 27
by solving the equation we find and consider the positive roots
x = 15 people
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there were 15 people in the group.