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Answer :
To solve the problem of determining which equation models the wages of someone earning [tex]$6.25 per hour, let's break down the situation:
1. Identify the Variables:
- \( y \) represents the total earnings in dollars.
- \( x \) represents the number of hours worked.
2. Relationship Between Variables:
- If someone earns $[/tex]6.25 per hour, there is a direct relationship between the hours worked and the earnings. Specifically, the earnings ([tex]\( y \)[/tex]) are equal to the number of hours worked ([tex]\( x \)[/tex]) multiplied by the hourly wage ([tex]$6.25).
3. Write the Equation:
- For each hour worked, the person earns $[/tex]6.25. Thus, the total earnings equation is:
[tex]\[
y = 6.25 \times x
\][/tex]
4. Evaluate the Options:
- Option A: [tex]\( x = 6.25x \)[/tex] – This doesn't make sense, as it implies that the hours worked equals itself multiplied, which is not logical.
- Option B: [tex]\( x = 625y \)[/tex] – Here, this would mean hours equals 625 times the earnings, which reverses the relationship.
- Option C: [tex]\( y = 625x \)[/tex] – This suggests earnings are 625 times the hours, which misstates the hourly rate.
- Option D: [tex]\( y = 6.25x \)[/tex] – This correctly reflects that earnings are 6.25 times the hours worked.
5. Conclusion:
- The correct equation that models this wage scenario is [tex]\( y = 6.25x \)[/tex], corresponding to option D. This correctly captures that the total earnings are a product of the hourly rate ($6.25) and the number of hours worked ([tex]\( x \)[/tex]).
1. Identify the Variables:
- \( y \) represents the total earnings in dollars.
- \( x \) represents the number of hours worked.
2. Relationship Between Variables:
- If someone earns $[/tex]6.25 per hour, there is a direct relationship between the hours worked and the earnings. Specifically, the earnings ([tex]\( y \)[/tex]) are equal to the number of hours worked ([tex]\( x \)[/tex]) multiplied by the hourly wage ([tex]$6.25).
3. Write the Equation:
- For each hour worked, the person earns $[/tex]6.25. Thus, the total earnings equation is:
[tex]\[
y = 6.25 \times x
\][/tex]
4. Evaluate the Options:
- Option A: [tex]\( x = 6.25x \)[/tex] – This doesn't make sense, as it implies that the hours worked equals itself multiplied, which is not logical.
- Option B: [tex]\( x = 625y \)[/tex] – Here, this would mean hours equals 625 times the earnings, which reverses the relationship.
- Option C: [tex]\( y = 625x \)[/tex] – This suggests earnings are 625 times the hours, which misstates the hourly rate.
- Option D: [tex]\( y = 6.25x \)[/tex] – This correctly reflects that earnings are 6.25 times the hours worked.
5. Conclusion:
- The correct equation that models this wage scenario is [tex]\( y = 6.25x \)[/tex], corresponding to option D. This correctly captures that the total earnings are a product of the hourly rate ($6.25) and the number of hours worked ([tex]\( x \)[/tex]).
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