Can you solve for x?

Question

[$s$]   [$u$]  [$r$]  [$q$]  [$22$]  [$r$] , [$q$]  [$22$]  [$p+2k$]  [$100-7k$] ,
[$q$]  [$k$]  [$3q$]  [$t$]  [$100-r$]  [$u$] , [$21$]  [$p+s-k$]  [$q$]  [$3p+k$]  [$23$] ,
[$p+s$]  [$22$][$2p+s$]  [$u$]  [$s$]  [$4s$]  [$u$] , [$k$]  [$r-s+k$] [$100-r-s$] [$p$] [$3q$][$12$],
[$q$] [$100-r$] [$u-s$] [$23$] [$p$] [$12$][$r$] [$t$].
                                              -x

[  ] lies between 1 and 100(extremes included)
$p+q+r+s+t+u+k=199$

$p,q,r,s,t,u,k$ are all distinct
$p,q,s,t,k$ are odd,
$r,u$ even

$q,t$ are primes
$u$ is largest
$k$ is smallest

The multiple $p\times q\times r\times s\times t\times u\times k$ does not have any of $p,q,r,s,t,u$ or $k$.

Hint:

Extremes included can mean that either p,q,r,s,t,u,k ...is 1 or 100...

Hint2:

22 = 'GO'

Hint3:

s 9 || q 19 || u 56 || r 52 || k 1 || t 29 || p 33

Answer 1

x is:

The poet, William Butler Yeats.

And the puzzle itself is:

A rendering of his poem, The Lake Isle of Innisfree, where each word has been replaced by a number repesenting its value in A1Z26.

I was only able to work this out after Hint 3 gave away the values of s, q, u, r, k, t and p. Plugging these into the mathematics gave:

9-56-52-19-22-52,
19-22-35-93,
19-1-57-29-48-56,
21-41-19-100-23,
42-22-75-56-9-36-56,
1-44-39-33-57-12,
19-48-47-23-33-12-52-29.

Armed with the knowledge from Hint 2:

We know that some of the 22's can be replaced by 'GO'. In A1Z26 'GO' is worth 22 points. Coincidence? I thought not... So I tried calculating the A1Z26 values of common words like 'and' and 'the' and slotted those in where they fitted, noting particularly that 1 would likely be A and 9 I:

I-56-52-and-go-52,
And-go-to-93,
And-a-57-29-48-there,
Of-41-and-100-23,
42-(go)-75-56-I-36-there,
A-44-for-the-57-12,
And-48-47-in-the-12-52-29.

Finally, Google was my friend!

Searching for poem "and go to" led me to The Lake Isle of Innisfree and all numeric values panned out!

I will arise and go now,
And go to Innisfree,
And a small cabin build there,
Of clay and wattles made,
Nine bean rows will I have there,
A hive for the honey bee,
And live alone in the bee-loud glade.

BOOM! Which all meant that 'x' must be:

Its creator, the poet William Butler Yeats, since this is how a poet's name often appears at the end of their published work, following a short dash. Phew, solved!

Answer 2

I feel like there is more to it than this, as I'm not sure how the X comes into play, but...

Possible values are: $p=23$, $q = 31$, $r = 16$, $s = 25$, $t = 37$, $u = 54$, and $k = 13$. Each of the values exist within brackets, so they need to be inclusively between 1 and 100. The operations within the brackets ($100-7k$, $100-r$, $r-s+k$, etc.) all also lie inclusively between 1 and 100. Following the rest of the parameters - $p+q+r+s+t+u+k \rightarrow 23+31+16+25+37+54+13=199$, they are all distinct, $p,q,s,t,k$ are odd and $r,u$ are even, $q,t$ are primes, $u$ is the largest and $k$ is the smallest. Finally, $p\times q\times r\times s\times t\times u\times k = 23\times 31\times 16\times 25\times 37\times 54\times 13=7407784800$, which doesn't have any of the numbers within it.