Question

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Answer 1

ok on the first one.

the 2nd one is tricky, because you could call the difference 25-x or
x-25 and you get two different answers.

but in either case, I am not getting -50

Answer 2

no, I do get -50

as a check
2*(-50 - 25) = 2*-75 = -150
and
3* -50 = -150

Answer 3

though we get a nicer number if we did
2(25-n) = 3n
50 -2n = 3n
50 = 5n
n= 10

Answer 4

It's ambiguous.

For example, I can ask what is the difference between 4 and 8
and what is the difference between 8 and 4 ?

maybe we assume the answer is always positive, so if we get a negative answer, we do it the other way round?

Answer 5

you got the correct answers.

if you solve for the "middle" number you have
n-2 + n + n+2 = 51
notice the left side sums to 3n so you have 3n= 51, n= 17
and remember that is the middle number, so the sequence is 15,17,19

similarly
3n = -18
n= -6

and we have -8 , -6, -4

Answer 6

it's n=+10

if we assume n is smaller than 25 we would do
2(25-n)= 3n
50 -2n = 3n
50= 5n
10 = n

if n is 10 the difference between n and 25 is 15
2*15 is 30
and 3n is 30

so it works.

if we assume n is bigger than 25 we would do n-25
if we work that out, we get n= -50
it works algebraically , but if we *assume* the difference is always a positive number, we rule out this case.

Answer 7

no. I am not following you.

I assume the "rule" is the difference between two numbers is always positive
(this isn't really math, it's more English. Because if I ask you what is the difference between 3 and 4 you would say 1, and if I ask you what is the difference between 4 and 3 , you would still say 1... so it seems we always pick the bigger number minus the smaller to find the difference)

Answer 8

if we write (n-25) we are assuming that n is bigger than 25
but when we solve it we get n= -50 which is smaller than 25
(and the difference is negative)

so we just don't use that answer, because (probably) the questioner was assuming the difference would be positive.

But unless they say what they mean, we are just guessing. But n=10 does seems like a nicer answer.