Problem 64 - Algebra and Trigonometry

Question

Company A pays \(\$ 23,000\) yearly with raises of \(\$ 1200\) per year. Company B pays \(\$ 26,000\) yearly with raises of \(\$ 800\) per year. Which company will pay more in year \(10 ?\) How much more?

Step-by-Step Solution

Answer

Company B will pay more in the 10th year. The difference will be \$400.

Step 1: Calculate Total Salary for Company A in Year 10

The formula for the nth term of an arithmetic series is \(a + (n - 1) * d\), where \(a\) is the first term, \(d\) is the common difference, and \(n\) is the number of terms. For company A, the first term (a) is \$23,000, the common difference (d) is \$1200 and the number of terms (n) is 10. Plugging these values into the formula yields \(23,000 + (10 - 1) * 1200\) which evaluates to \$32,800.

Step 2: Calculate Total Salary for Company B in Year 10

Using the same strategy and formula as in step 1, but this time for Company B. Here, \(a = \$26,000\), \(d = \$800\), and \(n = 10\). The 10th term of the salary will be \(26,000 + (10 - 1) * 800\), which is \$33,200.

Step 3: Compare the salaries and find the difference

The aim is to determine which company will pay more in year 10 and by how much. Company B's 10 year salary (\$33,200) is more than Company A's (\$32,800). Hence, Company B pays more. The difference in the salary paid by the companies in the 10th year is \$33,200 - \$32,800 = \$400.