41. Tanya earns \( \$ 34,000 \) in her 1 st year at a job. She is given a raise of the same dollar amount each year, resulting in her earning \( \$ 38,080 \) in the 4th year at the job. What is the total of Tanya's earnings during her 4 years at the job? A. \( \$ 106,080 \) B. \( \$ 136,000 \) C. \( \$ 140,080 \) D. \( \$ 144,160 \) E. \( \$ 152,320 \)

To find the total of Tanya's earnings over her 4 years at the job, we need to determine the dollar amount of her annual raise. 1. Tanya's earnings in the 1st year = \( \$34,000 \) 2. Earnings in the 4th year = \( \$38,080 \) The difference between her 4th year earnings and 1st year earnings gives us the total raises over 3 years: \[ \$38,080 - \$34,000 = \$4,080 \] Since this is over 3 years, her annual raise is: \[ \frac{\$4,080}{3} = \$1,360 \] Now, we can determine her earnings for each year: - 1st year: \( \$34,000 \) - 2nd year: \( \$34,000 + \$1,360 = \$35,360 \) - 3rd year: \( \$35,360 + \$1,360 = \$36,720 \) - 4th year: \( \$36,720 + \$1,360 = \$38,080 \) Now we can add these amounts to find her total earnings over the 4 years: \[ \$34,000 + \$35,360 + \$36,720 + \$38,080 = \$144,160 \] So, the answer is **D. \( \$144,160 \)**. This total reflects not only Tanya's consistent financial growth but also the benefits of receiving regular raises – a motivating factor for many workers!