School trip ratio

One hundred seventy-five school pupils signed up for the school trip. The ratio of boys to girls was 9: 16. In the end, 19 registered students did not come on the trip, so the ratio of the number of participating boys and girls was 9: 17. How many boys and how many girls did not go on the trip?

Final Answer:

x =  9
y =  10

Step-by-step explanation:

$$\begin{gathered} n=175 \\ {n}_2=n-19=175-19=156 \\ A:B=9:16 \\ a:b=9:17 \\ A=\frac{9}{9+16}\cdot n=\frac{9}{9+16}\cdot 175=63 \\ B=n-A=175-63=112 \\ a=\frac{9}{9+17}\cdot n_2=\frac{9}{9+17}\cdot 156=54 \\ b=n_2-a=156-54=102 \\ x=A-a=63-54=9 \end{gathered}$$

$y=B-b=112-102=10$

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