A manager is responsible for ordering supplies for a shaved ice shop. The shop's inventory starts with 4,500 paper cups,

Question

A manager is responsible for ordering supplies for a shaved ice shop. The shop's inventory starts with $4,500$ paper cups, and the manager estimates that $70$ of these paper cups are used each day. Based on this estimate, in how many days will the supply of paper cups reach $1,700$ ?

A.

$40$

B.

$60$

C.

$80$

D.

$20$

Accepted Answer

Choice B is correct. It&rsquo;s given that the shop&rsquo;s inventory starts with 4,500 paper cups and that the manager estimates that 70 of these paper cups are used each day. Let x represent the number of days in which the estimated supply of paper cups will reach 1,700 . The equation 4,500 - 70 x = 1,700 represents this situation. Subtracting 4,500 from both sides of this equation yields - 70 x = - 2,800 . Dividing both sides of this equation by - 70 yields x = 40 . Therefore, based on this estimate, the supply of paper cups will reach 1,700 in 40 days. Choice A is incorrect. After 20 days, the estimated supply of paper cups would be 4,500 - 70 ( 20 ) , or 3,100 cups, not 1,700 cups. Choice C is incorrect. After 60 days, the estimated supply of paper cups would be 4,500 - 70 ( 60 ) , or 300 cups, not 1,700 cups. Choice D is incorrect. After 80 days, the estimated supply of paper cups would be 4,500 - 70 ( 80 ) , or - 1,100 cups, which isn't possible.

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