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Easy one

This topic has 5 expert replies and 1 member reply
manu.pant Senior | Next Rank: 100 Posts Default Avatar
Joined
04 May 2010
Posted:
33 messages

Easy one

Post Wed May 18, 2011 8:14 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A certain country had a total annual expenditure of
    $1.2 X 10^12 last year. If the population of the country
    was 240 million last year, what was the per capita
    expenditure?

    Ans is 5000, but I think it should be 500

    Source: OG12, Prob Solving 133

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    Post Wed May 18, 2011 8:38 pm
    manu.pant wrote:
    A certain country had a total annual expenditure of
    $1.2 X 10^12 last year. If the population of the country
    was 240 million last year, what was the per capita
    expenditure?

    Ans is 5000, but I think it should be 500

    Source: OG12, Prob Solving 133
    $1.2 X 10^12 = 12 * 10^11
    240 million = 240 * 10^6 = 24 * 10^7
    So, per capita expenditure = 12 * 10^11/24 * 10^7 = (1/2) * 10^4 = 0.5 * 10^4 = $5,000

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    Post Wed May 18, 2011 8:39 pm
    manu.pant wrote:
    A certain country had a total annual expenditure of
    $1.2 X 10^12 last year. If the population of the country
    was 240 million last year, what was the per capita
    expenditure?

    Ans is 5000, but I think it should be 500

    Source: OG12, Prob Solving 133
    Expenditure/Population:
    = (1.2 * 10^12)/(240 * 10^6)
    = (12 * 10^11)/(24 * 10^7)
    = (12/24)*(10^11/10^7)
    = 1/2 * 10^4
    = 5,000.

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    Post Sat Jun 27, 2015 5:30 am
    manu.pant wrote:
    A certain country had a total annual expenditure of
    $1.2 X 10^12 last year. If the population of the country
    was 240 million last year, what was the per capita
    expenditure?

    Ans is 5000, but I think it should be 500

    Source: OG12, Prob Solving 133
    A certain country had a total annual expenditure of $1.2 x 10^12 last year. If the population of the country was 240 million last year, what was the per capita expenditure?

    A) $500
    B) $1,000
    C) $2,000
    D) $3,000
    E) $5,000

    Solution:

    One key to solving this problem is to accurately translate what is being asked into a mathematical equation. We need to determine the “per capita expenditure," which is obtained by the formula:

    Per capita expenditure = (Total annual expenditure)/(Total population)

    The first step is to express 240 million as a number times a power of 10, since the other number is in such a format.

    240 million = 240,000,000

    Since we have a 24 with 7 zeroes we can write this number as:

    24 x 10^7

    Next, we adjust 1.2 x 10^12 to make it a more useful number in our expression.

    1.2 x 10^12 = 120 x 10^10

    We now can solve:

    Per capita expenditure = (Total annual expenditure)/(Total population)

    Per capita expenditure = (120 x 10^10)/(24 x 10^7)

    Per capita expenditure = 5 x 10^3

    Per capita expenditure = 5 x 1,000

    Per capita expenditure = 5,000

    Answer:E

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    Post Thu Jul 02, 2015 3:49 am
    5000

    Post Mon Aug 28, 2017 2:34 pm
    Quote:
    A certain country had a total annual expenditure of $1.2 x 10^12 last year. If the population of the country was 240 million last year, what was the per capita expenditure?

    (A) $ 500
    (B) $1,000
    (C) $2,000
    (D) $3,000
    (E) $5,000
    Let's use a nice rule that says: (ab)/(cd) = (a/c)(b/d)

    Per capita expenditure = (total expenditure of country)/(total population of country)
    = (1.2 x 10^12)/(240 million)
    = (1.2 x 10^12)/(240 x 10^6)
    = (1.2 x 10^3 x 10^9)/(240 x 10^6)
    = (1.2 x 10^3 x 10^9)/(240 x 10^6)
    = (1200 x 10^9)/(240 x 10^6)
    = (1200/240)(10^9/10^6)
    = (5)(10^3)
    = (5)(1000)
    = 5000

    Answer: E

    Cheers,
    Brent

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    Post Wed Aug 30, 2017 5:41 pm
    Quote:
    = (1.2 * 10¹²)/(240 million)
    = (1.2 * 10¹²)/(240 * 10⁶)
    = (1.2 * 10³ * 10⁹)/(240 * 10⁶)
    = (1.2 * 10³ * 10⁹)/(240 * 10⁶)
    = (1200 * 10⁹)/(240 * 10⁶)
    = (1200/240)(10⁹/10⁶)
    = (5)(10³)
    = (5)(1000)
    = 5000
    ftfy ^ ^

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