# Word Problem

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• Oct 29th 2008, 10:43 AM
Tomanator
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?
• Oct 29th 2008, 11:58 AM
masters
Quote:

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:

\$\displaystyle 16000+1500y=19300+950y\$
• Oct 29th 2008, 12:54 PM
Soroban
Hello, Tomanator!

Quote:

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 \$\displaystyle x\$ years.

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

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

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

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

Now solve for \$\displaystyle x.\$

• Oct 29th 2008, 01:04 PM
masters
Quote:

Originally Posted by Soroban
Hello, Tomanator!

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

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

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

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

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

Now solve for \$\displaystyle x.\$

Better explanation, Soroban. (Bow)
• Oct 29th 2008, 09:39 PM
Tomanator
Thank you both, great explination