1. The problem is a set of simple algebraic equations where we need to find the value of each variable. 2. The general formula used is to isolate the variable by performing inverse operations. For example, if the equation is $m + 13 = 20$, subtract 13 from both sides to get $m = 20 - 13$. 3. Let's solve the first equation step-by-step: Given: $m + 13 = 20$ Subtract 13 from both sides: $$m + \cancel{13} - \cancel{13} = 20 - 13$$ Simplifies to: $$m = 7$$ 4. Similarly, for the second equation: Given: $20 = f - 27$ Add 27 to both sides: $$20 + 27 = f - \cancel{27} + \cancel{27}$$ Simplifies to: $$f = 47$$ 5. For the third equation: Given: $3x = 102$ Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{102}{\cancel{3}}$$ Simplifies to: $$x = 34$$ 6. The rest of the variables are solved similarly: - $64 = 4e \Rightarrow e = \frac{64}{4} = 16$ - $t + 28 = 51 \Rightarrow t = 51 - 28 = 23$ - $r - 10 = 30 \Rightarrow r = 30 + 10 = 40$ - $p - 11 = 39 \Rightarrow p = 39 + 11 = 50$ - $\frac{y}{3} = 12 \Rightarrow y = 12 \times 3 = 36$ - $61 = 28 + n \Rightarrow n = 61 - 28 = 33$ - $21 = \frac{b}{8} \Rightarrow b = 21 \times 8 = 168$ - $95 = 5k \Rightarrow k = \frac{95}{5} = 19$ 7. Each variable is found by isolating it using inverse operations such as addition/subtraction or multiplication/division. Final answers: $$m=7, f=47, x=34, e=16, t=23, r=40, p=50, y=36, n=33, b=168, k=19$$