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Onyx starts a new job that offered a great signing bonus and hourly wage. Her first work cycle she worked 45 hours and her paycheck was $1,425 before taxes. Her second work cycle pay stub showed she had worked 85 hours total for the company and had earned $2,625 cumulatively (all together over the span of her employment) before taxes.



Let x represent the number of hours she’s worked cumulatively for the company. Let y represent the money she’s earned cumulatively before taxes.

Verified Answer :

Answer:

Step-by-step explanation:

To find the relationship between the number of hours worked (x) and the money earned before taxes (y), we can set up a system of equations based on the information provided.

Let's denote:

- \( x_1 \) as the number of hours worked in the first work cycle (45 hours).

- \( x_2 \) as the number of hours worked in the second work cycle (85 hours).

- \( y_1 \) as the money earned before taxes in the first work cycle ($1,425).

- @@MATH_TOKEN_4@@ as the money earned before taxes in the second work cycle ($2,625).

We have two equations:

1. \( x_1 + x_2 = x \) (Total hours worked = hours worked in the first cycle + hours worked in the second cycle)

2. \( y_1 + y_2 = y \) (Total money earned = money earned in the first cycle + money earned in the second cycle)

We can solve this system of equations:

Given:

- \( x_1 = 45 \)

- \( x_2 = 85 \)

- \( y_1 = 1425 \)

- \( y_2 = 2625 \)

1. \( 45 + 85 = x \)

  \( x = 130 \)

2. \( 1425 + 2625 = y \)

  \( y = 4050 \)

So, the relationship between the number of hours worked (x) and the money earned before taxes (y) can be represented by the equation:

\[ y = 31.15x \]

mathstudent55

Answer:

y = 30x + 75

Step-by-step explanation:

(45, 1425)

(85, 2625)

y = mx + b

m = (2625 - 1425)/(85 - 45)

m = 1200/40

m = 30

y = 30x + b

2625 = 30(85) + b

b = 75

y = 30x + 75

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