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Chapter 8: Problem 55

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?

Short Answer

Expert verified
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 by step solution

01

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: \[ A = 24,000 + 1,600*(10-1) \]
02

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.
03

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.

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