200 people were surveyed about which four seasons is their favorite. of those surveyed 1/8 selected spring 2/5 selected summer and 3/10 selected autumn . The remainder of the participants selected winter. how many people surveryed selected winter as their favorite season?A 25B 35C 60D 70E 80

Respuesta :

In order to find the number of people that selected winter, first let's find the corresponding fraction.

The sum of the fractions needs to be 1, so using the variable x to represent the fraction of people that selected winter, we have:

[tex]\begin{gathered} \frac{1}{8}+\frac{2}{5}+\frac{3}{10}+x=1 \\ \frac{5+16+12+40x}{40}=\frac{40}{40} \\ 40x+33=40 \\ 40x=7 \\ x=\frac{7}{40} \end{gathered}[/tex]

Now, to find the number of people, we just need to multiply this fraction by the total number of people:

[tex]\frac{7}{40}\cdot200=7\cdot5=35[/tex]

So the number of people that selected winter is 35, therefore the correct option is B.

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