Math  /  Data & Statistics

QuestionThe following table shows mean annual earnings for women and men by their highest achieved level of education. As a percentage, how much more does a man with a master's degree earn than a woman with a master's degree? Assuming the difference remains constant over a 40 -year career, how much more does the man earn than the woman? \begin{tabular}{|l|c|c|c|c|} \hline & \begin{tabular}{c} High \\ School \end{tabular} & \begin{tabular}{c} Associate's \\ degree \end{tabular} & \begin{tabular}{c} Bachelor's \\ degree \end{tabular} & \begin{tabular}{c} Master's \\ Degree \end{tabular} \\ \hline Women & $31,677\$ 31,677 & $39,604\$ 39,604 & $59,402\$ 59,402 & $76,106\$ 76,106 \\ \hline Men & $45,390\$ 45,390 & $59,250\$ 59,250 & $87,343\$ 87,343 & $114,652\$ 114,652 \\ \hline \end{tabular}
A man with a master's degree earns \square %\% more annually than a woman with a master's degree. (Round to the nearest whole number as needed.)

Studdy Solution

STEP 1

1. The earnings data provided in the table is accurate and representative.
2. We need to calculate the percentage increase in earnings from a woman with a master's degree to a man with a master's degree.
3. We assume the difference in earnings remains constant over a 40-year career to calculate the total difference in earnings over that period.
4. The percentage increase can be calculated using the formula: Percentage Increase=(Man’s EarningsWoman’s EarningsWoman’s Earnings)×100 \text{Percentage Increase} = \left( \frac{\text{Man's Earnings} - \text{Woman's Earnings}}{\text{Woman's Earnings}} \right) \times 100

STEP 2

1. Extract the earnings data for women and men with a master's degree.
2. Calculate the percentage increase in earnings for men compared to women.
3. Calculate the total additional earnings for men over a 40-year career.

STEP 3

Extract the earnings data for women and men with a master's degree.
Earnings for women with a master’s degree=$76,106\text{Earnings for women with a master's degree} = \$76,106 Earnings for men with a master’s degree=$114,652\text{Earnings for men with a master's degree} = \$114,652

STEP 4

Calculate the difference in earnings between men and women with a master's degree.
Difference in earnings=$114,652$76,106=$38,546\text{Difference in earnings} = \$114,652 - \$76,106 = \$38,546

STEP 5

Calculate the percentage increase in earnings for men compared to women.
Percentage Increase=($38,546$76,106)×100\text{Percentage Increase} = \left( \frac{\$38,546}{\$76,106} \right) \times 100

STEP 6

Perform the division and multiplication to find the percentage.
Percentage Increase=(38,54676,106)×10050.63%\text{Percentage Increase} = \left( \frac{38,546}{76,106} \right) \times 100 \approx 50.63\% Rounded to the nearest whole number, this becomes: Percentage Increase51%\text{Percentage Increase} \approx 51\%

STEP 7

Calculate the total additional earnings for men over a 40-year career.
Total additional earnings over 40 years=$38,546×40\text{Total additional earnings over 40 years} = \$38,546 \times 40

STEP 8

Perform the multiplication to find the total additional earnings.
Total additional earnings over 40 years=$38,546×40=$1,541,840\text{Total additional earnings over 40 years} = \$38,546 \times 40 = \$1,541,840
Solution: A man with a master's degree earns approximately 51%51\% more annually than a woman with a master's degree. Over a 40-year career, the man earns an additional \$1,541,840 compared to the woman.

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