Math Help - what is jk?

1. what is jk?

ok so here we go...

we have the set up which states that only students within a certain range, can use the trombone...

so 95 is less than equal to T which is less than equal to 185..

now this next part i found on the internet...but it was suggested that i find the middle of the range which is 140, and so i subtract 140 from each part of the setup???

so now i have this inequality that i need to rewrite with the use of absolute value bars, but the only problem is that i do not know how to set that up...any help would be appreciated and can you explain why i need to find the middle of the range and why is that being subtracted from either side. thanks

2. Re: what is jk?

we know that 95 ≤ w ≤ 185 (i am using w instead of T, to match the book).

what we want is something that looks like:

|w - j| ≤ k, which is the same as:

-k ≤ w - j ≤ k

if we add j to everything, we get:

-k + j ≤ w ≤ k + j, which is what we have:

k + j = 185
-k + j = 95

let's add the two equations, to get:

k + j + -k + j = 185 + 95

2j = 280

j = 140 (see where the 140 comes in?)

now we can find k:

k + j = 185

k + 140 = 185

k = 45

as a check, we verify the other equation as well:

-k + j = 95

-k + 140 = 95

-k = -45

k = 45.

now we know that:

95 ≤ w ≤ 185 is the same condition as:

-45 + 140 ≤ w ≤ 45 + 140

-45 ≤ w - 140 ≤ 45

|w - 140| ≤ 45.

it should be obvious what jk is now.

3. Re: what is jk?

Hello, slapmaxwell1!

Students are allowed to use the trampoline if they weigh from 95 to 185 pounds.
Express this restriction in the form $|w - j| \:\le\:k$
where $w$ is a student's weight, and $j$ and $k$ are constants.
What is $jk$?

Maybe a picture will clarify the situation.

. . $\begin{array}{ccccccc}\cdots & \bullet & --- & \circ & --- & \bullet & \cdots \\ & 95 && 140 && 185 \end{array}$

The middle of range is 140 pounds.
We can see that a student's weight must be
. . no more than 45 pounds away from the middle.

This can be written: . $|w - 140| \:\le\:45$

Hence: . $j = 140,\;k = 45$

Therefore: . $jk \;=\;140\cdot45 \;=\;6300$