Answered

Samir 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 Samir 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]\( y = 15x + 19 \)[/tex]
D. [tex]\( y = 19x + 15 \)[/tex]



Answer :

GinnyAnswer
To determine which equation correctly represents the relationship between the number of hours Samir works ([tex]\(y\)[/tex]) and the number of hours Mitul works ([tex]\(x\)[/tex]), let's break down the problem:

1. Identify Given Ratios:
- For every 19 hours that Mitul works, Samir works 15 hours.

2. Formulate the Relationship:
- We need to find [tex]\(y\)[/tex], the number of hours Samir works, in terms of [tex]\(x\)[/tex], the number of hours Mitul works.

3. Ratio Application:
- Since Samir works 15 hours for every 19 hours that Mitul works, we can set up the following proportion:
[tex]\[ \frac{y}{x} = \frac{15}{19} \][/tex]

4. Solve for [tex]\(y\)[/tex]:
- To express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex], we multiply both sides of the equation by [tex]\(x\)[/tex]:
[tex]\[ y = \frac{15}{19} x \][/tex]

Therefore, the equation that correctly models the relationship between the hours that Samir works and the hours that Mitul works is:
[tex]\[ y = \frac{15}{19} x \][/tex]

So, the correct choice from the given options is:
[tex]\[ y = \frac{15}{19} x \][/tex]

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