Average age

There are 20 students in the class. Several are 12 years old, and others are 13 years old. Find out how old is twelve when the average age of a class is:

a) 12.5 years

b) 12.75 years

c) 12.3 years

d) 12.35 years

Final Answer:

a =  10
b =  5
c =  14
d =  13

Step-by-step explanation:

$$\begin{gathered} \frac{12\cdot a+13\cdot (20-a)}{20}=12.5 \\ 12\cdot a+13\cdot (20-a)=20\cdot 12.5 \\ a=10 \end{gathered}$$

$$\begin{gathered} 12\cdot b+13\cdot (20-b)=20\cdot 12.75 \\ b=5 \end{gathered}$$

$$\begin{gathered} 12\cdot c+13\cdot (20-c)=20\cdot 12.3 \\ c=14 \end{gathered}$$

$$\begin{gathered} 12\cdot d+13\cdot (20-d)=20\cdot 12.35 \\ d=13 \end{gathered}$$

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