1. ## Word Problem

If someone can give me a hint of how to set up the formula that would be great. I believe its a Arithmetic sequence formula, and I can figure it out just by adding the sequence for the answer to be 6 years.

Mei's salary starts at $16000 per year with annual raises of$1500. Janet's starting salary is $19300 with annual raises of$950 per year. After how many years will the two women be earning the same salary?

2. Originally Posted by Tomanator
If someone can give me a hint of how to set up the formula that would be great. I believe its a Arithmetic sequence formula, and I can figure it out just by adding the sequence for the answer to be 6 years.

Mei's salary starts at $16000 per year with annual raises of$1500. Janet's starting salary is $19300 with annual raises of$950 per year. After how many years will the two women be earning the same salary?
Hello Tomanator,

Here's a big hint:

$16000+1500y=19300+950y$

3. Hello, Tomanator!

Mei's salary starts at $16,000 per year with annual raises of$1,500.
Janet's starting salary is $19,300 with annual raises of$950 per year.
After how many years will the two women be earning the same salary?

Mei's salary is $16,000 plus a$1,500 raise per year for $x$ years.

. . In her $x^{th}$ year, her salary is: . $16,\!000 + 1,\!500x$ dollars.

Janet's salary is $19,300 plus a$950 raise per year for $x$ years.

. . In her $x^{th}$ year, her salary is: . $19,\!300 + 950x$ dollars.

When are the two salaries equal? . . $16,\!000 + 1,\!500x \;=\;19,\!300 + 950x$

Now solve for $x.$

4. Originally Posted by Soroban
Hello, Tomanator!

Mei's salary is $16,000 plus a$1,500 raise per year for $x$ years.

. . In her $x^{th}$ year, her salary is: . $16,\!000 + 1,\!500x$ dollars.

Janet's salary is $19,300 plus a$950 raise per year for $x$ years.

. . In her $x^{th}$ year, her salary is: . $19,\!300 + 950x$ dollars.

When are the two salaries equal? . . $16,\!000 + 1,\!500x \;=\;19,\!300 + 950x$

Now solve for $x.$
Better explanation, Soroban.

5. Thank you both, great explination