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If 50 one-cent coins were stacked on top...

If 50 one-cent coins were stacked on top of each other in a column, the column would be approximately `3 7/8` inches tall. At this rate, which of the following is closest to the number of one-cent coins it would take to make an 8-inch-tall column?

A

75

B

100

C

200

D

390

Text Solution

Verified by Experts

The correct Answer is:
B
A column of 50 stacked one-cent coins is about `3 7/8` inches tall, which is slightly less than 4 inches tall. Therefore a column of stacked one-cent coins that is 4 inches tall would contain slightly more than 50 one-cent coins. It can then be reasoned that because 8 inches is twice 4 inches, a column of stacked one-cent coins that is 8 inches tall would contain slightly more than twice as many coins, that is, slightly more than 100 one-cent coins. An alternate approach is to set up a proportion comparing the column height to the number of one-cent coins , or `(3 7/8 "inches")/("50 coins") = "8 inches"/"x coins"` , where x is the number of coins in an 8-inch-tall column. Multiplying each side of the proportion by 50x gives `3 7/8x=400`. Solving for x gives `x=(400xx8)/31` , which is approximately 103. Therefore, of the given choices, 100 is closest to the number of one-cent coins it would take to build an 8-inch-tall column.
Choice A is incorrect. A column of 75 stacked one-cent coins would be slightly less than 6 inches tall. Choice C is incorrect. A column of 200 stacked one-cent coins would be more than 15 inches tall. Choice D is incorrect. A column of 390 stacked one-cent coins would be over 30 inches tall.
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