QuestionAn employee earns \$9.25/hour and \$8 for every 20 transformers. Find their hourly earnings for 36 hours and 380 transformers.

Studdy Solution

STEP 1

Assumptions1. The employee is paid $9.25 per hour. . The employee receives a bonus of$ 8.00 for every20 transformers assembled.
3. Last week, the employee worked36 hours and assembled380 transformers.
4. We need to find the actual earnings per hour of the employee, rounded to the nearest cent.

STEP 2

First, we calculate the total amount earned from hourly wages by multiplying the hourly wage by the number of hours worked.
$Hourly\, earnings = Hourly\, wage \\times Hours\, worked$

STEP 3

Now, plug in the given values for the hourly wage and hours worked to calculate the hourly earnings.
$Hourly\, earnings = \$9.25 \\times36$

STEP 4

Calculate the hourly earnings.
$Hourly\, earnings = \$9.25 \\times36 = \$333$

STEP 5

Next, we calculate the total bonus earned from assembling transformers. First, we find the number of bonuses earned by dividing the total number of transformers assembled by20.
$Number\, of\, bonuses = Transformers\, assembled /20$

STEP 6

Now, plug in the given value for the number of transformers assembled to calculate the number of bonuses.
$Number\, of\, bonuses =380 /20$

STEP 7

Calculate the number of bonuses.
$Number\, of\, bonuses =380 /20 =19$

STEP 8

Then, we calculate the total bonus earned by multiplying the number of bonuses by the bonus amount.
$Bonus\, earnings = Number\, of\, bonuses \\times Bonus\, amount$

STEP 9

Now, plug in the values for the number of bonuses and the bonus amount to calculate the bonus earnings.
$Bonus\, earnings =19 \\times \$8$

STEP 10

Calculate the bonus earnings.
$Bonus\, earnings =19 \\times \$8 = \$152$

STEP 11

Now that we have the hourly earnings and the bonus earnings, we can find the total earnings by adding these two amounts.
$Total\, earnings = Hourly\, earnings + Bonus\, earnings$

STEP 12

Plug in the values for the hourly earnings and the bonus earnings to calculate the total earnings.
$Total\, earnings = \$333 + \$152$

STEP 13

Calculate the total earnings.
$Total\, earnings = \$333 + \$152 = \$485$

STEP 14

Now that we have the total earnings, we can find the actual earnings per hour by dividing the total earnings by the number of hours worked.
$Actual\, earnings\, per\, hour = Total\, earnings / Hours\, worked$

STEP 15

Plug in the values for the total earnings and the hours worked to calculate the actual earnings per hour.
$Actual\, earnings\, per\, hour = \$485 /36$

STEP 16

Calculate the actual earnings per hour.
$Actual\, earnings\, per\, hour = \$485 /36 \approx \$13.47$ The factory employee actually earned approximately $13.47 per hour last week, rounded to the nearest cent.

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