DVD Club A DVD club offers four DVDs for dollar-sign 0.49 each plus shipping and handling and additional DVDs for dollar-sign 16.95 each plus shipping and handling. Shipping and handling is dollar-sign 2.31 per DVD. A discount retailer offers the same DVDs for dollar-sign 12.95each plus 7 % sales tax. What is the maximum number of DVDs that can be ordered from the club while keeping it a better deal than the discount retailer?

Jaylene Hunter

Jaylene Hunter

Answered question

2022-07-25

DVD Club A DVD club offers four DVDs for dollar-sign 0.49 each plus shipping and handling and additional DVDs for dollar-sign 16.95 each plus shipping and handling. Shipping and handling is dollar-sign 2.31 per DVD. A discount retailer offers the same DVDs for dollar-sign 12.95each plus 7 % sales tax. What is the maximum number of DVDs that can be ordered from the club while keeping it a better deal than the discount retailer?

Answer & Explanation

Franklin Frey

Franklin Frey

Beginner2022-07-26Added 15 answers

Solution: Cost of 4 DVDs form club
= 4 × ( 0.49 + 2.31 ) = $ 11.2
Let x numbers of additional DVDs are ordered from the club.
Then, cost of the additional DVDs
= ( 16.95 + 2.32 ) x = $ 19.27 x
Total cost of (x+4) DVDs = 11.2 x + 19.27 x = $ 30.47 x
Now at retailer cost of the same (4+x) DVDs
= ( 12.95 + 12.95 × 7 100 ) × ( 4 + x ) = ( 12.95 + 0.9065 ) × ( 4 + x ) = ( 13.8565 ) × ( 4 + x )
Thus, cost (4+x) DVDs from the retailer =$13.8565(4+x)
Now for the ordered from the club while keeping it a better deal than the discount retailer,
$ 30.47 x < $ 13.8565 ( 4 + x )
or 30.47 x 13.8565 x > 13.8565 × 4 16.6135 x < 55.426 x < 3.34
Thus (4+x) = (4+3) =7 DVDs
Therefore maximum 7 DVDs should be ordered from the club.

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