Amir works 15 hours for every 19 hours that Mitul works. If [tex]\( x \)[/tex] represents the number of hours that Mitul works and [tex]\( y \)[/tex] represents the hours that Amir works, which equation correctly models this relationship?

A. [tex]\( y = \frac{15}{19} x \)[/tex]
B. [tex]\( y = \frac{19}{15} x \)[/tex]
C. [tex]\( y = 15 x + 19 \)[/tex]
D. [tex]\( y = 19 x + 15 \)[/tex]



Answer :

To determine the correct equation that models the relationship between the hours worked by Amir and Mitul, we must analyze the given ratio statement: "Amir works 15 hours for every 19 hours that Mitul works."

Let:
- [tex]\( x \)[/tex] represent the number of hours that Mitul works.
- [tex]\( y \)[/tex] represent the number of hours that Amir works.

The relationship between Amir's and Mitul's working hours can be expressed as a ratio or proportion. Specifically, Amir works 15 hours for every 19 hours that Mitul works, which can be set up as:
[tex]\[ \frac{y}{x} = \frac{15}{19} \][/tex]

To transform this proportion into an equation, we can multiply both sides by [tex]\( x \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{15}{19} x \][/tex]

So, the equation that correctly models the relationship between the hours worked by Amir ([tex]\( y \)[/tex]) and Mitul ([tex]\( x \)[/tex]) is:
[tex]\[ y = \frac{15}{19} x \][/tex]

Therefore, the correct choice is the first option:
[tex]\[ y = \frac{15}{19} x \][/tex]