SOLUTION: Teacher generated question, not from a textbook. You are in charge of setting up a room for an awards banquet at your school. A total of 122 people will attend the banquet. Th

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Question 185026: Teacher generated question, not from a textbook.
You are in charge of setting up a room for an awards banquet at your school. A total of 122 people will attend the banquet. The school has tables that seat either 8 or 10 people. No empty seats are allowed. How many of each size table will you need to use to make sure everyone has a seat?
Can get to "8x + 10y = 122" but need to develop second equation to solve using elimination or substitution.
Thank you.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Teacher generated question, not from a textbook.
You are in charge of setting up a room for an awards banquet at your school.
A total of 122 people will attend the banquet. The school has tables that seat
either 8 or 10 people. No empty seats are allowed. How many of each size table
will you need to use to make sure everyone has a seat?
Can get to "8x + 10y = 122" but need to develop second equation to solve
using elimination or substitution.
:
That's the only equation you will get from the information given, however since
there are no empty seats, x and y have to be integers that will give 122.
:
simplify the equation by dividing by 2, re-write it:
4x + 5y = 61
5y = 61 - 4x
y = - x
choose a value for x and see if y is an integer, if it is that is a one solution
I found there are three solutions
x=4
y = - (4)
y = -
y =
y = 9; (32 + 90 = 122)
and
x = 9
y = - (9)
y = - x
y =
y = 5; (72 + 40 = 122)
and one more
x=14
y = - (14)
y = -
y =
y = 1; (112 +10 = 122)