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The population of Sheffield is 690,000 to the nearest thousand and the population of Nottingham is 730,000 to the nearest 1000.

Calculate the upper and lower bounds for the difference in population between Sheffield and Nottingham.

Please answer with clear instructions so that i can apply this to other questions

User Hzrari
by
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1 Answer

16 votes
16 votes

Answers:

lower bound = 39001

upper bound = 40999

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Step-by-step explanation:

You'll have to think backwards to find what values round to 690,000 when rounding to the nearest thousand.

It turns out that if x is on the interval
689,500 \le x \le 690,499, then x will round to 690,000 when rounding to the nearest thousand. The x refers to the population of Sheffield, so it's some integer in that range.

Through similar logic, if y is on the interval
729,500\le y \le 730,499 then it will round to 730,000 when rounding to the nearest thousand. This represents the population of Nottingham.

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Now let's say we go for the smallest possible value of x (689500) and the largest possible value of y (730499). This guarantees the two populations are the most spread out or distant from one another. Subtract those two values:

730,499 - 689,500 = 40,999

This is the largest difference possible of the two populations. It represents the upper bound, i.e. it's the ceiling.

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On the other hand, let's now say x is as big as possible (690499) and y will be as small as possible (729500). Subtract those values:

729,500 - 690,499 = 39,001

This is the lower bound. It's the smallest the difference can be. It's considered the floor.

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Let d be the difference in the populations. In other words, d = y-x

We found that the lower bound was 39,001 and the upper bound was 40,999

Meaning that


39,001 \le y-x \le 40,999

or


39,001 \le d \le 40,999

User RajibTheKing
by
3.0k points
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