School grade expression

There are p first-year students in the school. There are 18% fewer sophomores than first-year students. There are 7 more third graders than sophomores and twice as many fourth graders as first- and second-year students combined. Express the number of pupils in the 1st grade.

Final Answer:

x = 6.28p + 7

Step-by-step explanation:

$$\begin{gathered} r=100\%-18\%=1-\frac{18}{100}=0.82 \\ x=p+r\cdot p+(7+r\cdot p)+2\cdot (p+r\cdot p) \\ k=1+r\cdot 1+r\cdot 1+2\cdot (1+r\cdot 1)=1+0.82\cdot 1+0.82\cdot 1+2\cdot (1+0.82\cdot 1)=\frac{157}{25}=6\frac{7}{25}=6.28 \\ x=k\cdot p+7 \\ x=6.28p+7 \end{gathered}$$

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