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Suzan managed to get 40 points out of a possible 60 from the last paper. Her average number of points from the tests increased from 27 to 28 points. How many points should she have written if she wanted her overall average to rise to 29 points?

Correct answer:

x =  53

Step-by-step explanation:

$$\begin{gathered} p=27 \\ (p\cdot n+40)/(n+1)=28 \\ (p\cdot n+40)=28\cdot (n+1) \\ (27\cdot n+40)=28\cdot (n+1) \\ n=12 \\ n=\frac{12}{1}=12 \\ n=12 \\ (p\cdot n+x)=29\cdot (n+1) \\ (27\cdot 12+x)=29\cdot (12+1) \\ x=53 \\ x=\frac{53}{1}=53 \\ x=53 \\ \text{ Verifying Solution: } \\ {a}_1=\frac{p\cdot n+40}{n+1}=\frac{27\cdot 12+40}{12+1}=28 \\ {a}_2=\frac{p\cdot n+x}{n+1}=\frac{27\cdot 12+53}{12+1}=29 \end{gathered}$$

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