Bill Gates Proportions II

[Feature photo above by Remy Steinegger via Wikimedia Commons (CC BY 2.0).]

Another look at the Bill Gates proportion… Even though I couldn’t find any data on his real income, I did discover that the median American family’s net worth was $93,100 in 2004 (most of that is home equity) and that the figure has gone up a bit since then. This gives me another chance to play around with proportions.

So I wrote a sample problem for my Advanced Math Monsters workshop at the APACHE homeschool conference:

The median American family has a net worth of about $100 thousand. Bill Gates has a net worth of $56 billion. If Average Jane Homeschooler spends $100 in the vendor hall, what would be the equivalent expense for Gates?

In the last post, I explained that a proportion sets two ratios equal to each other. Each ratio must compare similar thing to similar thing in the same order. In this case, we are interested in the ratio “Expense : Net Worth.”

\frac{Jane's \: Expense}{Jane's \: Net \: Worth}   =   \frac{Bill's \: Expense}{Bill's \: Net \: Worth}

Substitute the numbers:

\frac{100}{100,000}   =   \frac{x}{56,000,000,000}

Multiply both sides by 56 billion:

\frac{100 \times 56,000,000,000}{100,000}   =   x

Simplify the fraction by canceling zeros:

56,000,000   =   x

I can’t resist books, and the vendor hall is temptation beyond bearing. Like the crafty politician promoting his latest tax plan, I absolve myself with a pious claim: “It’s for the children.” If I am not careful next weekend, I may spend the equivalent of $100 million or more, in Bill Gates dollars.

3 thoughts on “Bill Gates Proportions II

  1. Question – first you mention the $93k and then in the problem you say that the median is “about a million.” Is there a decimal point missing somewhere?

  2. Duh! Yes, there’s a decimal point missing in my brain—thank you for catching my mistake. How embarrassing when I do something like that in public! I’ll go back and make the correction.

    It reminds me of the old joke: Ask someone, “What is 9 + 1? … What is 99 + 1? … What is 909 + 1?” Give the person time to answer each question. When led on like this, most people will say, “1,000” to that last one.

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