10. A florist sells candles and vases. There must be at least 5 items in each shipment, but there cannot be more than 12 in a shipment. Additionally, the shipment must weigh less than 35 pounds. Each shipment container weighs 5 pounds, plus 2 pounds of packing material. A candle weighs 3 pounds and a vase weighs 1.5 pounds. a) Write a system of inequalities to represent the constraints on the number of items that can be included in one shipment. b) Suppose that John wants to buy 12 candles. Would he be able to get them all in one shipment? Explain how you determined your answer. c) Suppose Mary wants to buy 6 candles and 6 vases. Would she be able to get them all in one shipment? Explain how you determined your answer.
let x be the number of candles and y be the number of vases.
since there must be at least 5 items in the shipment , therefore,
there can not be more than 12 items in the shipment , therefore,
combining we get
weight of 1 candles is 3 pounds and weight of 1 vases is 1.5 pounds .
therefore, total weight of x candles and y vases is given by
weight of the shipment must be less than 35 pounds, therefore, where 5 pounds is the weight of the shipment container and 2 pounds is weight of packing material .
(a)
the system of inequalities is given by
(b) to check whether John will be able to get the 12 candles in one shipment , substitute and in the inequalities .
gives which is true.
check the second inequality
which is false.
Hence John will not be able to receive 12 candles in 1 shipment.
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