Timothy

Timothy is 56 4/5 inches tall. Theresa is 1 1/6 inches shorter than Timothy, and Jane is 1 1/3 inches shorter than Theresa. How tall is Jane?

Correct answer:

J =  54 ³⁄₁₀ = 543/10 in

Step-by-step explanation:

$$\begin{gathered} T_1=56\frac{4}{5}=56+\frac{4}{5}=\frac{56\cdot 5+4}{5}=\frac{280+4}{5}=\frac{284}{5}=56.8\text{in} \\ {d}_1=1\frac{1}{6}=1+\frac{1}{6}=\frac{1\cdot 6+1}{6}=\frac{6+1}{6}=\frac{7}{6}\doteq 1.1667\text{in} \\ {d}_2=1\frac{1}{3}=1+\frac{1}{3}=\frac{1\cdot 3+1}{3}=\frac{3+1}{3}=\frac{4}{3}\doteq 1.3333\text{in} \\ {T}_2=T_1-d_1=\frac{284}{5}-\frac{7}{6}=\frac{1704}{30}-\frac{35}{30}=\frac{1704-35}{30}=\frac{1669}{30}\doteq 55.6333\text{in} \\ J=T_2-d_2=\frac{1669}{30}-\frac{4}{3}=\frac{1669}{30}-\frac{40}{30}=\frac{1669-40}{30}=\frac{1629}{30}=\frac{543}{10}\text{in}=54\frac{3}{10}\text{in}=54.3\text{in} \end{gathered}$$

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