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Solved on Nov 03, 2023

Ethan earns 9.80perhour.Inoneweekheworks40hours,9hoursat9.80 per hour. In one week he works 40 hours, 9 hours at \14.70 14.70 per hour, and 3 hours at $19.60\$ 19.60 per hour. Calculate his gross wage.

STEP 1

Assumptions1. Ethan earns $9.80 per hour for regular time. . In one week, he works40 hours of regular time.
3. He also works9 hours at time and a half.
4. He works an additional3 hours at double time.

STEP 2

First, we need to calculate Ethan's earnings for the regular time hours. We can do this by multiplying his hourly wage by the number of regular hours he works.
arningsregular=Hourly wagetimesRegular hoursarnings_{regular} = Hourly\, wage \\times Regular\, hours

STEP 3

Now, plug in the given values for the hourly wage and regular hours to calculate the earnings for regular time.
arningsregular=$9.80times40arnings_{regular} = \$9.80 \\times40

STEP 4

Calculate the earnings for regular time.
arningsregular=$9.80times40=$392arnings_{regular} = \$9.80 \\times40 = \$392

STEP 5

Next, we need to calculate Ethan's earnings for the time and a half hours. We can do this by multiplying his hourly wage by1.5 (to account for the time and a half) and then by the number of time and a half hours he works.
arnings1.5time=Hourly wagetimes1.5timesHours1.5timearnings_{1.5 time} = Hourly\, wage \\times1.5 \\times Hours_{1.5 time}

STEP 6

Now, plug in the given values for the hourly wage and time and a half hours to calculate the earnings for time and a half.
arnings1.5time=$9.80times1.5times9arnings_{1.5 time} = \$9.80 \\times1.5 \\times9

STEP 7

Calculate the earnings for time and a half.
arnings1.5time=$9.80times1.5times9=$132.30arnings_{1.5 time} = \$9.80 \\times1.5 \\times9 = \$132.30

STEP 8

Next, we need to calculate Ethan's earnings for the double time hours. We can do this by multiplying his hourly wage by2 (to account for the double time) and then by the number of double time hours he works.
arnings2time=Hourly wagetimes2timesHours2timearnings_{2 time} = Hourly\, wage \\times2 \\times Hours_{2 time}

STEP 9

Now, plug in the given values for the hourly wage and double time hours to calculate the earnings for double time.
arnings2time=$9.80times2times3arnings_{2 time} = \$9.80 \\times2 \\times3

STEP 10

Calculate the earnings for double time.
arnings2time=$9.80times2times3=$58.80arnings_{2 time} = \$9.80 \\times2 \\times3 = \$58.80

STEP 11

Now that we have the earnings for regular time, time and a half, and double time, we can add these together to find Ethan's total gross wage for the week.
Gross wage=arningsregular+arnings.5time+arningstimeGross\, wage =arnings_{regular} +arnings_{.5 time} +arnings_{ time}

STEP 12

Plug in the values for the earnings from regular time, time and a half, and double time to calculate the gross wage.
Gross wage=$392+$132.30+$58.80Gross\, wage = \$392 + \$132.30 + \$58.80

STEP 13

Calculate the gross wage.
Gross wage=$392+$132.30+$58.80=$583.10Gross\, wage = \$392 + \$132.30 + \$58.80 = \$583.10than's gross wage for the week is $583.10.

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