Problem 55 - College Algebra

Question

Company A pays \(\$ 24,000\) yearly with raises of \(\$ 1600\) per year. Company B pays \(\$ 28,000\) yearly with raises of \(\$ 1000\) per year. Which company will pay more in year \(10 ?\) How much more?

Step-by-Step Solution

Answer

By plugging the years into the given formula, we get: \[ A = 24,000 + 1600 * (10 - 1) = 38,400 \] and \[ B = 28,000 + 1000 * (10 - 1) = 37,000 \]. So, Company A will pay more in the 10th year by \$1400.

Step 1: Calculating the Total Salary in Company A for a Decade

We should start this calculation by using the salary in the first year, which is \$24,000 and add the annual increment of \$1,600 multiplied by the year number (since each year the raise increases due to the annual increment). By following this process, for 10 years, a formula for company A will look like this: \[ A = 24,000 + 1,600*(10-1) \]

Step 2: Calculating the Total Salary in Company B for a Decade

In a similar manner, the salary of 10 years in company B is calculated using the formula: \[ B = 28,000 + 1,000*(10-1) \]. Here we perform the same operation, adjusting for the different starting salary and annual raises.

Step 3: Finding the Difference in Salaries

Once we have the totals for both companies, we can subtract the total of company B from that of company A to find the difference, i.e., which company pays more and by how much. If the result is negative, Company B pays more. If the result is positive, Company A pays more.