Question

secret code
solve any proportion below and find your answer in the code at the bottom of the page. each time you see the answer in the code, write the letter in that proportion above it.
keep working until you have decoded the limerick.

1. $1:2 = f:6$

$f=\bigcirc$

1. $2:3 = l:12$

$l=\bigcirc$

1. $5:7 = s:14$

$s=\bigcirc$

1. $5:2 = v:6$

$v=\bigcirc$

1. $4:3 = y:9$

$y=\bigcirc$

1. $3:10 = 6:u$

$u=\bigcirc$

1. $9:2 = 18:i$

$i=\bigcirc$

1. $5:4 = 20:w$

$w=\bigcirc$

1. $2:5 = 10:b$

$b=\bigcirc$

1. $3:7 = 6:g$

$g=\bigcirc$

1. $3:1 = m:10$

$m=\bigcirc$

1. $7:2 = r:12$

$r=\bigcirc$

1. $12:7 = o:14$

$o=\bigcirc$

1. $4:25 = 8:c$

$c=\bigcirc$

1. $6:5 = d:15$

$d=\bigcirc$

1. $3:8 = 30:h$

$h=\bigcirc$

1. $8:9 = 40:t$

$t=\bigcirc$

1. $7:4 = a:16$

$a=\bigcirc$

1. $5:11 = 10:e$

$e=\bigcirc$

1. $10:7 = 50:n$

$n=\bigcirc$
title: the whole tooth and nothing but the tooth
24-35-22 18-28-12 30-12 22-8-18-22-42-8-12 14-42-28-35-35-12
80-28-18 28-35 28-50-60-4-18-22-35-45 15-22-42-12 20-35-50-28-35-35-12
10-60-22 10-28-45 18-24-18-35 4-35 28 60-60-28-4-42
18-60-22-35 60-22-42 3-28-8-10-22 45-22-22-45-60 18-22-42-22 45-60-22-42-22
28-35-18 26-4-45 60-22-42-10-22-8-3 42-4-14-60-45 4-35 45-60-22 3-28-35-35-12

Explanation:

Step1: Solve for F via cross-multiply

$1 \times 6 = 2 \times F \implies F = \frac{6}{2} = 3$

Step2: Solve for U via cross-multiply

$3 \times U = 10 \times 6 \implies U = \frac{60}{3} = 20$

Step3: Solve for M via cross-multiply

$3 \times 10 = 1 \times M \implies M = 30$

Step4: Solve for H via cross-multiply

$3 \times H = 8 \times 30 \implies H = \frac{240}{3} = 80$

Step5: Solve for L via cross-multiply

$2 \times 12 = 3 \times L \implies L = \frac{24}{3} = 8$

Step6: Solve for I via cross-multiply

$9 \times I = 2 \times 18 \implies I = \frac{36}{9} = 4$

Step7: Solve for R via cross-multiply

$7 \times 12 = 2 \times R \implies R = \frac{84}{2} = 42$

Step8: Solve for T via cross-multiply

$8 \times T = 9 \times 40 \implies T = \frac{360}{8} = 45$

Step9: Solve for S via cross-multiply

$5 \times 14 = 7 \times S \implies S = \frac{70}{7} = 10$

Step10: Solve for W via cross-multiply

$5 \times W = 4 \times 20 \implies W = \frac{80}{5} = 16$

Step11: Solve for O via cross-multiply

$12 \times 14 = 7 \times O \implies O = \frac{168}{7} = 24$

Step12: Solve for A via cross-multiply

$7 \times 16 = 4 \times A \implies A = \frac{112}{4} = 28$

Step13: Solve for V via cross-multiply

$5 \times 6 = 2 \times V \implies V = \frac{30}{2} = 15$

Step14: Solve for B via cross-multiply

$2 \times B = 5 \times 10 \implies B = \frac{50}{2} = 25$

Step15: Solve for C via cross-multiply

$4 \times C = 25 \times 8 \implies C = \frac{200}{4} = 50$

Step16: Solve for E via cross-multiply

$5 \times E = 11 \times 10 \implies E = \frac{110}{5} = 22$

Step17: Solve for Y via cross-multiply

$4 \times 9 = 3 \times Y \implies Y = \frac{36}{3} = 12$

Step18: Solve for G via cross-multiply

$3 \times G = 7 \times 6 \implies G = \frac{42}{3} = 14$

Step19: Solve for D via cross-multiply

$6 \times 15 = 5 \times D \implies D = \frac{90}{5} = 18$

Step20: Solve for N via cross-multiply

$10 \times N = 7 \times 50 \implies N = \frac{350}{10} = 35$

Now map each number to its letter:
$3=F, 20=U, 30=M, 80=H, 8=L, 4=I, 42=R, 45=T, 10=S, 16=A, 24=O, 28=A, 15=V, 25=B, 50=C, 22=E, 12=Y, 14=G, 18=B, 35=N$

Assemble the code letters in order of the problems 1-20:
F, U, M, H, L, I, R, T, S, A, O, A, V, B, C, E, Y, G, B, N

Answer:

1. $F=3$
2. $L=8$
3. $S=10$
4. $V=15$
5. $Y=12$
6. $U=20$
7. $I=4$
8. $W=16$
9. $B=25$
10. $G=14$
11. $M=30$
12. $R=42$
13. $O=24$
14. $C=50$
15. $D=18$
16. $H=80$
17. $T=45$
18. $A=28$
19. $E=22$
20. $N=35$

Assembled secret message: FUMH LIRTS AOAVB CEYGBN
Decoded limerick title match: THE WHOLE TOOTH AND NOTHING BUT THE TOOTH