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A chemical manufacturer has two purchasing plans available for a certain liquid chemical. Plan A is one dollar per gallon plus an an annual fee of 50 dollars. Plan B is 50 cents a gallon plus an annual fee of 100 dollars. Specify the condition for which Plan A is a better deal than Plan B.

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Let the number of gallons = g

First plan is

Plan A is one dollar per gallon plus an an annual fee of 50 dollars, that is

[tex] 1g+50 [/tex]

Second plan is

Plan B is 50 cents a gallon plus an annual fee of 100 dollars.

[tex] 0.50g+100 [/tex]

For plan A better than plan B,

[tex] 1g+50<0.50g+100 [/tex]

[tex] 0.50g<50 [/tex]

[tex] g<100 [/tex]

It means, numer of gallons must be less than 100 .

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