Answered: If you spread a billion dollars worth…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

If you spread a billion dollars worth of 1-dollar bills over the ground, how many square miles would they cover? (The length and the width of a 1-dollar bill are 6.14 and 2.61 inches, respectively.)

Expert Solution

Step 1

We have length and width of 1-dollar bill

length : $l =$ $6.14$ inch

width : $w = 2.61$ inch

Area of 1-dollar bill is given as

$A = l \times w$

$A =$ $6.14 \times 2.61$ $i n^{2}$

$A =$ $16.0254$ $i n^{2}$

Number of 1-dollar bills =1 billion

1 billion = $10^{9}$

Area of 1billion dollar bills will be

$A_{1} = A \times 10^{9}$

$A_{1} =$ $16.0254 \times 10^{9}$ $i n^{2}$

Using conversion unit

1 mile = 63360 inches

1 inch = $\frac{1}{63360}$ mile

$1$ $i n^{2} =$ ${(\frac{1}{63360})}^{2}$ $m i^{2}$

1 $i n^{2} =$ $\frac{1}{4014489600}$ $m i^{2}$

So,

$A_{1} =$ $\frac{16.0254 \times 10^{9}}{4014489600}$ $m i^{2}$

$A_{1} =$ $\frac{160254000}{4014489}$ $m i^{2}$

$A_{1} = 3.99188$ $97$ $m i^{2}$

Rounding off two decimal places

$A_{1} = 3.99$ $m i^{2}$

Area of 1 billion dollar bills = 3.99 square miles

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