Kip and Celia began working for the same company in 1997. Celia earned $19,000 per year, and Kip earned $16,000 per year. Each year Kip received a $1,500 raise and celia recived a $1,000 raise.
a. In what year will they earn the same amount of money.
b. What will be thier annual salary that year.
Kip = 1500x + 16000
Celia = 1000x + 19000
a) when is Kip = Celia ?
1500x + 16000 = 1000x + 19000
x = ..... , year = 1997 + x
b) sub the above solution for x into either of the two equations.
To find the year when Kip and Celia will earn the same amount of money, we can create equations for their annual salaries over time. We can start by defining the salaries of Kip and Celia in terms of the number of years since 1997.
Let's denote the number of years since 1997 as "x". Based on the information given, we can write the equations for their salaries as follows:
Kip's salary: $16,000 + $1,500 * x
Celia's salary: $19,000 + $1,000 * x
To find the year when they will earn the same amount, we need to set their salaries equal to each other and solve for x:
$16,000 + $1,500 * x = $19,000 + $1,000 * x
Now let's solve this equation step by step:
Subtract $1,000 * x from both sides:
$16,000 + $500 * x = $19,000
Subtract $16,000 from both sides:
$500 * x = $3,000
Divide both sides by $500:
x = 6
Hence, they will earn the same amount of money in the 6th year since 1997.
To find their annual salary in that year, we substitute x = 6 into either of the original equations. Let's use Celia's equation:
Celia's salary: $19,000 + $1,000 * 6 = $19,000 + $6,000 = $25,000
Therefore, in the 6th year since 1997, both Kip and Celia will earn $25,000 per year.