Two workers were hired to begin work at the same time

Two workers were hired to begin work at the same time. Worker A’s contract called for a starting salary of $20,000 with an increase of $800 after each year of employment. Worker B’s contract called for a starting salary of $15,200 with an increase of $2,000 after each year of employment. If x represents the number of full years’ employment (that is, the number of yearly increases each worker has received), which of the following equations could be solved to determine the number of years until B’s yearly salary equals A’s yearly salary?

1. 20,000 + 800x = 15,200 + 2,000x
2. 20,000 + 2,000x = 15,200 + 800x
3. (20,000 + 800)x = (15,200 + 2,000)x
4. (2,000 + 800)x = 20,000 - 15,200
5. (2,000 - 800)x = 20,000 + 15,200

Answer

The correct answer is A.

For x years of full years’ employment after being hired, Worker A’s starting salary $20,000 increases by $800 per year and Worker B’s starting salary $15,200 increases by $2,000 per year.

After x years, Worker A’s salary has increased by $800x and Worker B’s salary has increased by $2,000x.

So, for x years of full years’ employment after being hired, Worker A’s yearly salary is represented by the expression 20,000 + 800x and Worker’s B’s salary is represented by the expression 15,200 + 2,000x.

These 2 yearly salaries are equal at the value of x for which the equation 20,000 + 800x = 15,200 + 2,000x is true.