SOLUTION: Ashley estimates that there are a marbles in a jar. Harry, who knows the actual number of marbles in the jar, b, notes that Ashley’s estimate is within 15 marbles (inclusive) of
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Question 1190443: Ashley estimates that there are a marbles in a jar. Harry, who knows the actual number of marbles in the jar, b, notes that Ashley’s estimate is within 15 marbles (inclusive) of the actual number of marbles. Which of the following inequalities represents the relationship between Ashley’s estimate and the actual number of marbles in the jar?
a) -15≤a-b≤15
b) a≤b+15
c) a≥b-15
d) a+b≥15 Found 2 solutions by Boreal, math_tutor2020:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! It has to be A.
There are two possibilities for the within 15--below or above. Only A takes this into account. B and C imply that it is unidirectional, and adding both estimate an actual number doesn't lead to anything useful.
|a-b| <=15 would work fine, also.
The difference represents how far off Ashley is.
For example, if she guesses a= 10 marbles but there's actually b = 7 marbles, then she would be a-b = 10-7 = 3 marbles off.
For cases when b is larger than a, like a = 7 and b = 10, we have
a-b = 7-10 = -3
We can't have a negative distance. We want to be able to express this gap as some positive number or zero.
This is where absolute value comes in.
|a-b| ensures that the difference is never negative.
The lowest it can go is 0.
It represents the distance from a to b on the number line.
To be within 15 marbles means that the distance |a-b| is 15 or smaller
Put another way: the worst Ashley could guess is that she's 15 too high or 15 too low compared to the actual count.
This leads us to
That directly points to based on the rule that is equivalent to for any positive number k.
(