Jerry is a judge. He hears 555 cases every 2\dfrac382 8 3 ​ 2, start fraction, 3, divided by, 8, end fraction hours. Jerry hears cases at a constant rate. How many cases does he hear per hour?

Accepted Solution

Answer: [tex]2\frac{2}{19}[/tex] cases per hour.Step-by-step explanation: Let be "x" the number of cases Jerry hears  per hour. According to the information provided in the exercise, you know that he hears 5 cases every [tex]2\frac{3}{8}[/tex] hours. Convert from mixed number  to improper fraction. The procedure is: -  Multiply the whole number part by de the denominator of the fraction. - Add the product to the numerator. - The denominator does not change. Then: [tex]2\frac{3}{8}=\frac{(2*8)+3}{8}=\frac{19}{8}[/tex]  Now you can write the following proportion: [tex]\frac{5}{\frac{19}{8}}=\frac{x}{1}[/tex] Solving for "x", you get: [tex]x=\frac{40}{19}[/tex] Make the conversion to mixed number: - Dividing the numerator 40 by the denominator 19 you get a quotient of  2 (This will be the whole number part) - The remainder you get is 2 (This will be the numerator). - The denominator does not change. Then: [tex]x=2\frac{2}{19}[/tex]