This is a 3-part question.
There are a total 210 grams yarn. It will be difficult-to-impossible to get more yarn that will match.
Madeline Tosh Merino Light in Clematis
The sweater consists of Back (B), Left Front (F1), Right Front (F2), two sleeves (S) and Ruffle (R’) which wraps all the way around the bottom, fronts, and collar. S and R’ both contain short row ruffles which should be the same depth.
The body, consisting of B + F1 + F2, has used up 101 grams of yarn.
(A) Is there enough yarn to complete the project? What is the yarn deficit?
B = 98 caston + [56 rows even] + [cast off 8 each end twice for armhole] + [armhole dec to 78 over 4 rows] + [even 82r ]+ [cast off 12 each end 4 times for shoulders] + 30 bindoff
= 98 + [98 * 56] + [(98 * 1) + (90 * 1)] + [(82+78)*4/2] + [78 * 82] + [78 + 66 + 54 + 42] + 30
=98 + 5488 + 98 + 90 + 320 + 6396+ 78 + 66 + 54 + 42 + 31
B = 12760 stitches
F = 30 caston + [inc to 42 over 12 rows] + [inc to 50 over 16rows] + [29 rows even] + b[indoff 8] + [19 rows even] + [decrease to 24 over 36 rows] + [31 rows even] + [bind off 12 + 1 row even + bind off 12]
= 30 + [(30 + 42) * 12 / 2] + [(42 + 50) * 16 / 2] + [50*29] + [50 *1] + [42 * 19] + [(42 + 24) * 36 / 2] + [24 * 31] + [24 + 12 + 12]
=30 + 432 + 736 + 1450 + 50 + 798+1188+ 744+ 24 + 12 + 12
F = 5476 stitches
TOTAL knitted stitches
= 2 F + 1 B
= 2(5476) + 1(12760)
= 23712 stitches knitted so far
Find exchange rate from stitches to milligrams (use milligrams instead of grams to make easier)
Y = stitches per mg of yarn = 23712st/101000mg = .23477 st/mg
Stitches still required if knit as pattern written = (2S + R’)
S = {[nonruffle part]} + [ruffle short rows]
= {[Increase 16 to 43 st over 34 rows] + [32 rows even ]+ [decrease 43 to 16 st over 34 rows]} + [short rows 15 stitches wide of 2 rows every 2 regular rows]
= {[(16 + 43) * 34/2] + [43 x 32] + [(43 + 16) * 34/2]} + [ 2*15 * (16 + 17 + 16)]
= 1003 + 1376 + 1003 + 510 + 480 + 510
S = 4852
Ruffle R' requires 264 repeats of R
R’ = 264 R
R = {nonruffle part} + {ruffle short rows}
= {30*2} + {15 * 2}
= 60 + 30
R = 90
R’ = 264 * 90 = 23760
2S + R’ = (2*4852 + 23760)
33462 Stitches still required if knitted as written
mg yarn required = 33462/Y
= 33462 (1 mg/.23477 st) =
= 142,539 mg yarn still required if knitted as written
142,539 mg exceeds the remaining yarn of 109,000mg. There is not enough yarn to finish the project as written. The yarn deficit is 33.5 grams.
(B) How much do the short-row ruffles need to be shortened (in depth, not length) to be able to complete the project with the available yarn?
Ruffle depth = Z
Remaining stitches available = X = 109000mg (.23477st/1mg) = 25590 stitches remaining
S = [nonruffle part] + [ruffle short rows]
= [Increase 1 + Z to 18 + Z st over 34 rows] + [16 + Z *32 rows even] + decrease 16 + Z to 18 + Z st over 34 rows] + short rows Z stitches wide of 2 rows every 2 regular rows
= 34(1+Z+18+Z)/2 + 32(16+Z) + 34(1+Z+18+Z)/2
= 34 + 64Z + 612 + 512 + 32Z + 34 + 64Z + 612
= 160Z + 1804
R’ = 264 R
R = (15+Z)*2 + Z * 2
= 30+2Z +2Z
=4Z+30
R’ = 264 * Z = 264(4Z+30)
R’ = 1056Z + 7920
X = 2S + R’
= 2(160Z + 1804) + 1056Z + 7920
= 360Z + 3608 + 1056Z + 7920
= 1416Z + 11528
25590 = 1416Z + 11528
14062 = 1416Z
Z = 9.93
This project could be completed with the remaining yarn if the ruffle is decreased to 9-10 stitches wide.
(C) Now for the hard part: Will this sweater look loserish if the ruffle is decreased by 30%, from 15 stitches to 10 stitches wide?
Even in a copy of a picture of a reprint of a copy of the original vintage pattern, the sweater looks nicer than the modern version. It probably has to do with the corset underneath. Hmm.
What should I do? Knit the ruffles shorter and block them out as much as possible? Put the project on hold and try to find more yarn? Stripe with a slightly different yarn? Something else?
Answers welcome!
PS: This is for all those people who said that algebra wasn't useful in real life, and also for all the people who say there is no art to knitting