QuestionMark earns \$1,650/month. New job pays \$9.80/hour + overtime. Find overtime hours to match weekly earnings.

Studdy Solution

STEP 1

Assumptions1. Mark Adler's monthly salary at his current job is $1,650. His new job pays$ 9.80 per hour3. He gets paid time and a half for all hours over36 per week at his new job4. We are trying to find how many hours of overtime he needs to work at his new job to earn the same amount per week as his current job

STEP 2

First, we need to find Mark's weekly salary at his current job. We can do this by dividing his monthly salary by4 (assuming there are4 weeks in a month).
$Weekly\, salary = Monthly\, salary /4$

STEP 3

Now, plug in the given value for the monthly salary to calculate the weekly salary.
$Weekly\, salary = \$1,650 /$

STEP 4

Calculate the weekly salary.
$Weekly\, salary = \$1,650 /4 = \$412.50$

STEP 5

Next, we need to calculate how much Mark earns in a week at his new job without any overtime. We can do this by multiplying his hourly wage by36.
$Weekly\, earnings\, without\, overtime = Hourly\, wage \\times36$

STEP 6

Now, plug in the given value for the hourly wage to calculate the weekly earnings without overtime.
$Weekly\, earnings\, without\, overtime = \$9.80 \\times36$

STEP 7

Calculate the weekly earnings without overtime.
$Weekly\, earnings\, without\, overtime = \$9.80 \\times36 = \$352.80$

STEP 8

Now, we need to find how much Mark earns for each hour of overtime. This is time and a half of his hourly wage.
$vertime\, wage = Hourly\, wage \\times1.5$

STEP 9

Now, plug in the given value for the hourly wage to calculate the overtime wage.
$vertime\, wage = \$9.80 \\times.5$

STEP 10

Calculate the overtime wage.
$vertime\, wage = \$9.80 \\times.5 = \$14.70$

STEP 11

Finally, we need to find how many hours of overtime Mark needs to work to earn the same amount as his current job. We can do this by subtracting his weekly earnings without overtime from his weekly salary at his current job, and then dividing by his overtime wage.
$vertime\, hours = (Weekly\, salary - Weekly\, earnings\, without\, overtime) / Overtime\, wage$

STEP 12

Now, plug in the values for the weekly salary, weekly earnings without overtime, and overtime wage to calculate the overtime hours.
$vertime\, hours = (\$412.50 - \$352.80) / \$14.70$

STEP 13

Calculate the overtime hours.
$vertime\, hours = (\$412.50 - \$352.80) / \$.70 =.05 \, hours$ Mark needs to work approximately.05 hours of overtime each week to earn the same amount per week as his current job.

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