question_answer 1)

                A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Answer:

                Let the machine fill \[x\] bottles in five hours. We put the given information in the form of a table as shown below:             Number of bottles filled               840         \[x\] Number of hours                             6              5 More the number of hours, more the number of bottles would be filled. So, the number of bottles filled and the number of hours are directly proportional to each other.                 So, \[\frac{{{x}_{1}}}{{{x}_{2}}}=\frac{{{y}_{1}}}{{{y}_{2}}}\] \[\Rightarrow \]               \[\frac{840}{{{x}_{2}}}=\frac{6}{5}\]        \[\Rightarrow \]               \[6{{x}_{2}}=840\times 5\] \[\Rightarrow \]               \[{{x}_{2}}=\frac{840\times 5}{6}\] \[\Rightarrow \]               \[{{x}_{2}}=700\] Hence, 700 bottles will be filled.