Question 1168326: An online furniture store sells chairs for $200 each and tables for $500 each. Every day, the store can ship no more than 29 pieces of furniture and must sell at least $8800 worth of chairs and tables. If 14 chairs were sold, determine all possible values for the number of tables that the store must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of chairs
y = number of tables.
x + y <= 29
200x = revenue from x number of chairs
500y = revenue from y number of tables
200x + 500y >= 8800
when x = 14, ...
x + y <= 29 becomes 14 + y <= 29
subtract 14 from both sides of this inequality to get:
y <= 15
200x + 500y >= 8800 becomes:
200 * 14 + 500y >= 8800
simplify to get:
2800 + 500y >= 8800
subtract 2800 from both side of this inequality to get:
500y >= 8800 - 2800
simplify to get:
500y >= 6000
divide both sides of this inequality to get:
y >= 6000/500
simplify to get:
y >= 12
you have two requirements for y when x = 14.
they are y >= 12 and y <= 15.
your possible values of y are 12, 13, 14, 15
these 4 values of y satisfy the requirement that x + y <= 29 and 200x + 500y >= 8800 when x = 14.
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