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?
Correct answer: B. 100
- A. 75
- B. 100
- C. 200
- D. 390
Explanation
Choice B is correct. 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(7/8) x = 400. Solving for x gives x = 400 x 8 / 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.
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