Question

Stacie is choosing between two careers. Working for company A, Stacie will make $45,000 the first year and will receive an additional $1,500 per year for each year worked. Working for company B, Stacie will make $42,000 the first year, and she will receive an additional $1,800 per year for each year worked. The expressions representing each company’s total pay over 30 years are shown below.
How much more will company B pay over 30 years?
$12,000
$40,500
$49,200
$49,500

Answer 1

The expression in company B represents that is is in arithmetic progression where first term is 42000 and common difference is 1800 . So we have to use the formula of sum of n terms which is

$S=\frac{n}{2}(2a +(n-1)d)$

Where a is the first term, n is the nth term, d is the common difference

On substituting there values,we will get

$S =\frac{30}{2}(2*42000+(30-1)1800)$

= 15(84000+52200) = 15*136200 =2043000

And for company A, it is

$S= \frac{30}{2}(2*45000+(30-1)1500 ) = 15(90000+43500)=2002500$

Difference between them =2043000-2002500= 40500

So the correct option is the second option .