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QuestionRandi earned \$18,400, \$19,700, and \$21,600. What are her total earnings for 3 years, average earnings, and next year's target for \$21,000 average?

Studdy Solution

STEP 1

Assumptions1. Randi's earnings for the first year are 18,400.Randi′searningsforthesecondyearare18,400. Randi's earnings for the second year are 19,7003. Randi's earnings for the third year are 21,6004.Weareaskedtofindthetotalearningsforthethreeyears,theaverageearningsperyear,andtheamountsheneedstoearninthefourthyeartohaveanaverageof21,6004. We are asked to find the total earnings for the three years, the average earnings per year, and the amount she needs to earn in the fourth year to have an average of 21,000 over four years.

STEP 2

First, let's calculate the total amount Randi earned for the three years. We can do this by adding her earnings for each year.
Total earnings=arningsyear1+arningsyear2+arningsyearTotal\, earnings =arnings_{year1} +arnings_{year2} +arnings_{year}

STEP 3

Now, plug in the given values for the earnings in each year to calculate the total earnings.
Total earnings=$18,400+$19,700+$21,600Total\, earnings = \$18,400 + \$19,700 + \$21,600

STEP 4

Calculate the total earnings for the three years.
Total earnings=$18,400+$19,700+$21,600=$59,700Total\, earnings = \$18,400 + \$19,700 + \$21,600 = \$59,700

STEP 5

Now that we have the total earnings for the three years, we can find the average earnings per year by dividing the total earnings by the number of years (3).
Average earnings=Total earnings/Number of yearsAverage\, earnings = Total\, earnings / Number\, of\, years

STEP 6

Plug in the values for the total earnings and the number of years to calculate the average earnings per year.
Average earnings=$59,700/3Average\, earnings = \$59,700 /3

STEP 7

Calculate the average earnings per year.
Average earnings=$59,700/3=$19,900Average\, earnings = \$59,700 /3 = \$19,900

STEP 8

To find out how much Randi would need to earn next year so that her four-year average is $21,000, we first calculate the total amount she would need to have earned over four years. This can be done by multiplying the desired average by the number of years.
Total earnings4 years=Desired averagetimesNumber of yearsTotal\, earnings_{4\, years} = Desired\, average \\times Number\, of\, years

STEP 9

Plug in the values for the desired average and the number of years to calculate the total earnings for four years.
Total earnings4 years=$21,000times4Total\, earnings_{4\, years} = \$21,000 \\times4

STEP 10

Calculate the total earnings for four years.
Total earnings4 years=$21,000times4=$84,000Total\, earnings_{4\, years} = \$21,000 \\times4 = \$84,000

STEP 11

Now, subtract the total earnings for the first three years from the total earnings for four years to find out how much Randi needs to earn in the fourth year.
arningsyear4=Total earnings4 years−Total earnings3 yearsarnings_{year4} = Total\, earnings_{4\, years} - Total\, earnings_{3\, years}

STEP 12

Plug in the values for the total earnings for four years and the total earnings for three years to calculate the earnings for the fourth year.
arningsyear4=$84,000−$59,700arnings_{year4} = \$84,000 - \$59,700

STEP 13

Calculate the earnings for the fourth year.
arningsyear=$84,000−$59,700=$24,300arnings_{year} = \$84,000 - \$59,700 = \$24,300Randi needs to earn 24,300nextyearsothatherfour−yearaverageis24,300 next year so that her four-year average is 21,000.

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