Question

Cherie receives 2 different job offers after graduating job a offers Cherie a salaried position where she will earn 35,000 total a year job b offers Cherie an hourly position where she will earn 24 per hour as well as an annual bonus of 500 the system of equations w=35,000 w=24h+500 represents this situation where h is the number of hours Cherie works and w is her total wages solve using subsitution and interpret the solution

Answer 1

Answer:

h = 1437.5

If Cherie chooses Job B, she will need to work 1,437.5 hours per year to earn the same total wages offered by Job A.

Step-by-step explanation:

Cherie receives 2 different job offers after graduating.

• Job A offers Cherie a salaried position where she will earn a total of $35,000 per year.
• Job B offers Cherie an hourly position where she will earn $24 per hour as well as an annual bonus of $500.

The following system of equations represents this situation, where h is the number of hours Cherie works, and w is her total wages:

$\begin{cases}w = 35000\\w=24h+500\end{cases}$

To solve the system of equations using substitution, we can substitute the second equation into the first equation:

$24h+500=35000$

Subtract 500 from both sides of the equation:

$24h+500-500=35000-500$

$24h=34500$

Divide both sides of the equation by 24:

$\dfrac{24h}{24}=\dfrac{34500}{24}$

$h=1437.5$

Therefore, if Cherie chooses Job B, she will need to work 1,437.5 hours per year to earn the same total wages offered by Job A.

Given that 1,437.5 hours per year is approximately 27.6 hours per week, this option gives Cherie the flexibility to potentially earn more by working additional hours beyond the calculated 1,437.5 hours.

Answer 2

Answer:

$h = 1,437.5$ hours

Step-by-step explanation:

Let's solve the system of equations using substitution:

Given system of equations:

$\begin{cases} w = 35,000 ……\textsf{ Equation 1} \\\\ w = 24h + 500……\textsf{ Equation 2} \end{cases}$

For this, substitute value of w of first equation to second equation, we get

$35,000 = 24h + 500$

Now, let's solve for $h$ by substitution method:

For this, substitute value of w of first equation to second equation, we get

$24h = 35,000 - 500$

$24h = 34,500$

Divide both sides by 24:

$h = \dfrac{34,500}{24}$

Simplify the fraction:

$h = 1,437.5$

So, the solution is $h = 1,437.5$ hours.

Interpretation:

Cherie would need to work approximately 1,437.5 hours to make the same amount of money in job A, where she earns a fixed salary of $35,000.

This assumes that the hourly rate in job B is $24 per hour with an additional annual bonus of $500.