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expeople1 [14]
3 years ago
8

A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a f

ixed cost of $44,604.00 each year, and $27,396.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,715,760.00. How many people does the company intend to employ next year?
A.
731
B.
125
C.
61
D.
31
Mathematics
1 answer:
djyliett [7]3 years ago
4 0
The answer is C
First you subtract 44,604 from 1,715,760 to get 1,671,156 then you divide 1,671,156 by 27,396 to get 61 people
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If the series is made up of numbers in an arithmetic progression, you have

\displaystyle\sum_{n=1}^{18}a_n=\sum_{n=1}^{18}(a_1+(n-1)d)=18a_1+153d=4185

where a_1 is the first term and d is the common difference between terms.

Since the last term in the series is a_{18}=275, you have

a_{18}=a_1+(18-1)d\implies a_1+17d=275

Solve the system

\begin{cases}18a_1+153d=4185\\a_1+17d=275\end{cases}

and you'll find that the first term is a_1=190 (with d=5).
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