A test 3

A test of five light bulbs showed that they burned for the following lengths of time (in days): 17 2/3, 19 1/4, 20 1/2, 21, and 18 3/4. For how many days, on average, did the light bulbs burn?

Correct answer:

m =  19 ¹³⁄₃₀ = 583/30 h

Step-by-step explanation:

$$\begin{gathered} a=17\frac{2}{3}=17+\frac{2}{3}=\frac{17\cdot 3+2}{3}=\frac{51+2}{3}=\frac{53}{3}\doteq 17.6667\text{h} \\ b=19\frac{1}{4}=19+\frac{1}{4}=\frac{19\cdot 4+1}{4}=\frac{76+1}{4}=\frac{77}{4}=19.25\text{h} \\ c=20\frac{1}{2}=20+\frac{1}{2}=\frac{20\cdot 2+1}{2}=\frac{40+1}{2}=\frac{41}{2}=20.5\text{h} \\ d=21\text{h} \\ e=18\frac{3}{4}=18+\frac{3}{4}=\frac{18\cdot 4+3}{4}=\frac{72+3}{4}=\frac{75}{4}=18.75\text{h} \\ s=a+b+c+d+e=\frac{53}{3}+\frac{77}{4}+\frac{41}{2}+21+\frac{75}{4}=\frac{583}{6}\doteq 97.1667\text{h} \\ m=\frac{s}{5}=\frac{\frac{583}{6}}{5}=\frac{583}{30}\text{h}=19\frac{13}{30}\text{h}=19.4333\text{h} \end{gathered}$$

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