Swimming 79054

One hundred seventy-one pupils from the second to fourth years of primary school participated in swimming training. How many of them were from the fourth grade if there were 10% more third graders than second graders and 20% more fourth graders than third graders?

Final Answer:

d =  66

Step-by-step explanation:

$$\begin{gathered} r_1=100\%+10\%=1+\frac{10}{100}=1.1 \\ {r}_2=100\%+20\%=1+\frac{20}{100}=1.2 \\ b+c+d=171 \\ c=r_1\cdot b \\ d=r_2\cdot c \\ (c/r_1)+(d/r_2)+d=171 \\ ((d/r_2)/r_1)+(d/r_2)+d=171 \\ d+r_1\cdot d+d\cdot r_1\cdot r_2=171\cdot r_1\cdot r_2 \\ d+1.1\cdot d+d\cdot 1.1\cdot 1.2=171\cdot 1.1\cdot 1.2 \\ 3.42d=225.72 \\ d=\frac{225.72}{3.42}=66 \\ d=66 \end{gathered}$$

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