Answer:
x = 119
Step-by-step explanation:
To find the value of x for which the mixed number [tex]9 \frac{x}{200}[/tex] lies between 9.59 and 9.6, first express the mixed number as:
[tex]9 + \dfrac{x}{200}[/tex]
Given that this value is between 9.59 and 9.6, we can set up the following inequality:
[tex]9.59 < 9 + \dfrac{x}{200} < 9.6[/tex]
Subtract 9 from all parts of the inequality to isolate the fraction:
[tex]9.59 - 9 < 9+\dfrac{x}{200}-9 < 9.6 - 9\\\\\\0.59 < \dfrac{x}{200} < 0.60[/tex]
Next, eliminate the fraction by multiplying each part of the inequality by 200:
[tex]0.59\times 200 < \dfrac{x}{200} \times 200 < 0.60\times 200\\\\\\118 < x < 120[/tex]
Since x must be an integer, the possible value within this range is:
[tex]x=119[/tex]
To verify, substitute x = 119 back into the mixed number:
[tex]9 \dfrac{119}{200}[/tex]
Convert the fraction to a decimal:
[tex]9\dfrac{119}{200} = 9+\dfrac{119}{200}=9+0.595=9.595[/tex]
Since 9.595 is indeed between 9.59 and 9.6, the correct value of x is:
[tex]\Large\boxed{\boxed{x=119}}[/tex]
