Question

NEEEED HELP!! A company gives each new salesperson a commission of $300 for the sale of a new car. The salesperson will receive a $100 increase for each addition car the person sells that week, so the person gets $400 for the next sale that week. Which equation can find the number of cars a salesperson must sell to earn $4,200 in a week? Recall that a1/d(n-1) is equivalent to an

Answer 1

General Idea:

In an arithmetic sequence, to find the $n^{th}$ term, we need to use the below formula:

$a_n=a_1+(n-1)*d$

Here $a_n$ gives the $n^{th}$ term

$a_1$ gives the first term of sequence

d is the common difference and n is the number of terms in the sequence.

Applying the concept:

In our problem it is given that "A company gives each new salesperson a commission of $300 for the sale of a new car",

so $a_1=300$

"The salesperson will receive a $100 increase for each addition car the person sells that week"

so$d=100$

"find the number of cars a salesperson must sell to earn $4,200 in a week", this means that we need to find the value of n, when $a_n=4200$

Setting up the equation based on the arithmetic sequence formula, we get:

$4200=300+(n-1)*100\\ 4200=300+100n-100\\ 4200=200+100n\\ 100n+200=4200\\ 100n+200-200=4200-200\\ 100n=4000\\ \frac{100n}{100}=\frac{4000}{100} \\ n=40$

Conclusion:

New Salesperson has to sell 40 cars to earn $4200 in a week.