The expression: 553.7x + 27,966
Can be used to approximate the average annual salary in dollars of public school teacher in the year 1985 + x
What was the average teacher's salary in 1993?
In which year will the average salary reach $45,000?
plug and chug
p(1993) = 553.7(1993-1985) + 27,966
45000 = 553.7(x-1985) + 27,966
To find the average teacher's salary in a specific year, we can substitute the value of 'x' with the difference between that year and 1985 in the given expression: 553.7x + 27,966.
1. Average teacher's salary in 1993:
Since 1993 is 8 years after 1985, we substitute x with 8 in the expression:
Average teacher's salary in 1993 = 553.7(8) + 27,966
Calculate: (553.7 * 8) + 27,966 = 31,600.6 + 27,966 = $59,566.6 (rounded to the nearest dollar)
Therefore, the average teacher's salary in 1993 was approximately $59,567.
2. Year when the average salary reaches $45,000:
We need to find the value of 'x' when the expression equals $45,000. Rearranging the equation:
553.7x + 27,966 = 45,000
Subtracting 27,966 from both sides: 553.7x = 45,000 - 27,966 = 17,034
Dividing both sides by 553.7: x = 17,034 / 553.7 ≈ 30.75 (rounded to two decimal places)
Since 'x' represents the number of years after 1985, we find the approximate year by adding 30.75 to 1985:
Year when the average salary reaches $45,000 ≈ 1985 + 30.75 ≈ 2016
Therefore, the average salary will reach $45,000 approximately in the year 2016.