Math

QuestionMark Adler earns \$1,650 monthly. His new job pays \$9.80/hour with time and a half over 36 hours. How many overtime hours per week are needed to match his current weekly earnings?

Studdy Solution

STEP 1

Assumptions1. Mark Adler's previous monthly income was 1,650.Hisnewjobpays1,650. His new job pays 9.80 per hour3. He gets time and a half for all hours over36 per week in his new job4. We need to find how many hours of overtime he needs to work to earn the same amount per week as his previous job

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

Next, we need to calculate how much Mark earns in his new job without overtime. This is done by multiplying his hourly wage by36 (the number of hours he works without overtime).
Baseweeklyincome=Hourlywagetimes36Base\, weekly\, income = Hourly\, wage \\times36

STEP 6

Plug in the given values for the hourly wage to calculate the base weekly income.
Baseweeklyincome=$9.80times36Base\, weekly\, income = \$9.80 \\times36

STEP 7

Calculate the base weekly income.
Baseweeklyincome=$9.80times36=$352.80Base\, weekly\, income = \$9.80 \\times36 = \$352.80

STEP 8

Now, we need to find out how much Mark earns for each hour of overtime. This is done by multiplying his hourly wage by1.5 (time and a half).
vertimewage=Hourlywagetimes1.5vertime\, wage = Hourly\, wage \\times1.5

STEP 9

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

STEP 10

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

STEP 11

Finally, we need to find out how many hours of overtime Mark needs to work to earn the same amount as his previous job. This is done by subtracting his base weekly income from his previous weekly income and dividing by his overtime wage.
vertimehours=(PreviousweeklyincomeBaseweeklyincome)/Overtimewagevertime\, hours = (Previous\, weekly\, income - Base\, weekly\, income) / Overtime\, wage

STEP 12

Plug in the values for the previous weekly income, base weekly income, and overtime wage to calculate the overtime hours.
vertimehours=($412.50$352.80)/$14.70vertime\, hours = (\$412.50 - \$352.80) / \$14.70

STEP 13

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

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