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Percentage questions! HELP!

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Percentage questions! HELP!

by pirrum » Sun Jan 13, 2013 3:09 pm
Hi,

I've been trying to work out 4 of these percentage question - but I've become really stuck! Any help would be greatly appreciated.

Please could you also try and show workings too - so I can learn from my errors! I'm not sure the answers I have are actually correct.

Thanks.
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by Bill@VeritasPrep » Mon Jan 14, 2013 1:18 pm
For this first one, we are measuring percent change, so we have to know our original value and the amount of change.

The original value is total traffic 5 years ago: If we add up the individual regions, we come to a total of 2.1

The new value is total traffic now: if we add up the individual regions, we come to a total of 3.5

Our percent change formula is (new-old)/old * 100.

(3.5 - 2.1)/2.1 * 100

1.4/2.1 * 100

2/3 * 100

67%.
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by Bill@VeritasPrep » Mon Jan 14, 2013 1:28 pm
Here, we are comparing total distance on European flights between the two periods.

5 years ago: there were 300 million passengers traveling an average of 1000km each.

Today: average distance has decreased by 20% and is now .8*1000km = 800km per passenger. The number of passengers is now 900 million.

So our average distance is down by 20%, but the number of passengers is up 200%. This means that, overall, more distance has been covered. We can get rid of A, B, and C.

To find total distance, let's simplify our numbers. Since our passengers for each period are in the hundreds of millions, let's cancel out the extra zeroes. We can do the same for distance.

300 * 10 = 3,000

900 * 8 = 7,200

Percent change is then (7200 - 3000)/3000 * 100)

4200/3000 * 100

7/5 * 100 = 140%
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by Bill@VeritasPrep » Mon Jan 14, 2013 1:33 pm
For the greatest concentration of individuals per home, we have to look at population and home numbers for each region:

Northern: population 15.7m, total homes 11m (round to 16/11)

Midland: population 17.2m, total homes, 12.9m (round to 17/13)

Southern: population 21.3m, total homes 17.7m (round to 21/18)

Eastern: population 13.2m, total homes 12.9m (we can eliminate this one pretty easily: it has the same number of homes as the Midlands but fewer people)

Western: population 14.2m, total homes 14.9m (eliminate this one; it has less than 1 person per home, and we have 4 regions that have more than 1 person per home)

Northern has the highest concentration at nearly 1.5 people per home.
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by Bill@VeritasPrep » Mon Jan 14, 2013 1:41 pm
Does "with the price increasing by 10% in each region" mean that each successive region is 10% higher than the previous one? That's how I interpreted it.

Total capital can be found using the number of houses and the price per house.

Northern: 160,000, 11m

Midland: 176,000, 12.9m (higher price and more houses means that the Midlands clearly has more capital)

Southern: ~193,000, 17.7m (higher capital than Midland)

Eastern: ~212,000, 12.9m (higher price, but only by 10%, whereas this region has nearly 30% fewer homes. Southern still has more capital)

Western: ~233,000, 14.9m (close to Southern)

Western's home price is a bit over 20% higher than Southern's home price, but Western's population is less than 20% smaller than Southern's population.

Western has the most capital, I believe.
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