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Chapter 8: Problem 64

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?

Short Answer

Expert verified
In the 10th year, Company A will pay $600 more than Company B.

Step by step solution

01

Understand Salary Increment

First, understand that the salaries offered by both companies increase by a fixed amount every year. Company A's salary increases by $1200 per year and Company B's salary increases by $800 per year. These are examples of arithmetic sequences.
02

Find the 10th Term for Company A

We can use the formula for the nth term of an arithmetic sequence: \(a_n = a + (n-1)d\). For Company A, the first term \(a\) is $23000, and the common difference \(d\) is $1200. Substituting these values into the formula: \(a_{10} = 23000 + (10-1)*1200 = 23000 + 9*1200 = 33800\). Therefore, Company A will pay $33800 in the 10th year.
03

Find the 10th Term for Company B

For Company B, the first term \(a\) is $26000, and the common difference \(d\) is $800. Substituting these values into the formula: \(a_{10} = 26000 + (10-1)*800 = 26000 + 9*800 = 33200\). Therefore, Company B will pay $33200 in the 10th year.
04

Compare the 10th Term Salaries

To find out who pays more in the 10th year, simply subtract Company B's 10th year salary from Company A's 10th year salary: $33800 - $33200 = $600. Company A pays $600 more than Company B in the 10th year.

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Most popular questions from this chapter

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