SOLUTION: Ben's Digital Shop rents out DVDs. The manager observed that the weekly total number of rentals varies directly with the total inventory, and varies inversely with the cost of each

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Question 1171827: Ben's Digital Shop rents out DVDs. The manager observed that the weekly total number of rentals varies directly with the total inventory, and varies inversely with the cost of each rental. Last week's total rental is 300 DVDs when its inventory was 960 and the cost per rental was Php 25. If its inventory does not change, what would be the effect on the weekly total number rentals if the cost per rental will be increased to Php 30? Will it be beneficial for the store? Justify your answer.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
direct and inverse proportion formula for this problem is:
n = k * i / c
n = number of rentals
i = inventory
c = cost of each rental

n = 300
i = 960
c = 25

n = k * i / c becomes 300 = k * 960 / 25
solve k to get:
k = 300 * 25 / 960 = 7.8125

confirm by replacing k in the original equation to get:
300 = 7.8125 * 960 / 25 = 300
this confirms the value of k is good.

increasing the cost of each rental from 25 to 30 yields the following.
k remains the same at 7.8125
i remains the same at 960
formula becomes:
n = 7.8125 * 960 / 30
solve for n to get:
n = 250

based on the formula, raising the cost for each rental from 25 to 30 results in 50 fewer rentals.