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Chapter 1: Problem 75

The U.S. quarter has a mass of \(5.67 \mathrm{~g}\) and is approximately $1.55 \mathrm{~mm}$ thick. (a) How many quarters would have to be stacked to reach \(575 \mathrm{ft}\), the height of the Washington Monument? (b) How much would this stack weigh? (c) How much money would this stack contain? (d) The U.S. National Debt Clock showed the outstanding public debt to be $\$ 16,213,166,914,811\( on October \)28,2012 .$ How many stacks like the one described would be necessary to pay off this debt?

Short Answer

Expert verified
(a) 113,039 quarters are required to reach the height of the Washington Monument. (b) The weight of the stack would be 640.83 kg. (c) The total amount of money in the stack would be $28,259.75. (d) Approximately 573,492,330 stacks would be needed to pay off the U.S. National Debt as of October 28, 2012.

Step by step solution

01

Convert the height to millimeters

The height of the Washington Monument is given in feet (575 ft), we will convert it to millimeters to match the thickness's unit. 1 ft = 30.48 cm = 304.8 mm So, the height is 575 ft × 304.8 mm/ft = 175,260 mm.
02

Calculate the number of quarters required to reach this height

Given the thickness of one quarter is 1.55 mm, we can calculate the number of quarters required to reach 175,260 mm. Number of quarters = Height / Thickness = \( \frac{175{,}260}{1.55} \) = 113,039.
03

Calculate the weight of the stack

With the total number of quarters (113,039) and the mass of one quarter (5.67g), we can find the total mass (weight) of the stack. Total Weight = Number of quarters × Mass of one quarter = 113,039 × 5.67g = 640,831.13g.
04

Convert the weight to kilograms

To express the weight in a more common unit, convert grams to kilograms. 1 kg = 1000g Weight of the stack = 640,831.13g × 1 kg/1000g = 640.83 kg
05

Calculate the total amount of money in the stack

Since each quarter is worth 0.25 USD, we can find the total amount of money in the stack by multiplying the number of quarters by the value of one quarter. Total Amount = 113,039 × 0.25 USD = $28,259.75.
06

Calculate the number of stacks needed to pay off the National Debt

Given the National Debt is $16,213,166,914,811, we need to find how many stacks of the quarters described earlier would be required to pay off this debt. Number of stacks = National Debt / Amount in one stack = \( \frac{16{,}213{,}166{,}914{,}811}{28{,}259.75} \) ≈ 573,492,330. The exercise is solved, and the answers are as follows: a) 113,039 quarters are needed to reach the height of the Washington Monument. b) The stack of quarters would weigh 640.83 kg. c) The total amount contained in that stack would be $28,259.75. d) About 573,492,330 such stacks would be necessary to pay off the National Debt as of October 28, 2012.

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