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