A certain country had a total annual expenditure of
$1.2 × 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
Easy one
This topic has expert replies
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$1.2 × 10^12 = 12 * 10^11manu.pant wrote:A certain country had a total annual expenditure of
$1.2 × 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
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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Expenditure/Population:manu.pant wrote:A certain country had a total annual expenditure of
$1.2 × 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 * 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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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?manu.pant wrote:A certain country had a total annual expenditure of
$1.2 × 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) $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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Let's use a nice rule that says: (ab)/(cd) = (a/c)(b/d)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
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
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ftfy ^ ^= (1.2 * 10¹²)/(240 million)
= (1.2 * 10¹²)/(240 * 10�)
= (1.2 * 10³ * 10�)/(240 * 10�)
= (1.2 * 10³ * 10�)/(240 * 10�)
= (1200 * 10�)/(240 * 10�)
= (1200/240)(10�/10�)
= (5)(10³)
= (5)(1000)
= 5000