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

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.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

a = Ashley's estimate
b = true amount
a-b = difference of the two items

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.

Answer: Choice A

RELATED QUESTIONS
there are 300 marbles in a jar that contains only blue and red marbles. the number of... (answered by rm29924)
There were 5/7 as many red marbles as blue marbles in a jar. Dave took some blue marbles... (answered by josgarithmetic,Edwin McCravy,greenestamps)
the number of marbles in jar A is 4 times than in jar B.If 96 marbles are transferred... (answered by stanbon)
You have a jar of red marbles and a jar of yellow marbles. You take several(any number... (answered by checkley71)
You estimate that there are 48 marbles in a jar. The actual amount is 36 marbles. Find... (answered by stanbon)
there are 59 marbles in a jar. 21 are orange,15 are purple, and 23 are green.what is the... (answered by jsmallt9)
please help, A jar contains between 40 to 50 marbles. If the marbles are takem out of... (answered by josmiceli)
Jason has the same number of red and of blue marbles. He puts them in two jars so that... (answered by richwmiller)
A jar has twice as many red marbles as white marbles and the ratio of blue marbles to... (answered by Boreal)