One newspaper reported that the mayor received a salary increase of 5%. Another paper reported that the mayor's salary went up $2000. What was the mayor's salary before the increase?
My teacher gave us a hint.
y= 1.05x.
Here's an easy way to solve this. Let x equal the mayor's salary before his/her raise.
0.05x = 2,000
x = ???
Thank you!
You're welcome.
you can also use the formula ur teacher gave, y= 1.05x,
where x = 2000
y = is the new salary= 1.05x2000
The equation provided, y = 1.05x, suggests that the salary after the increase (y) is equal to the initial salary before the increase (x) multiplied by 1.05 (or 105%) to account for the 5% increase.
Let's use this equation to solve the problem:
We have two pieces of information from the newspaper reports. One report states that the mayor received a salary increase of 5%, while the other report states that there was a $2000 increase in the mayor's salary. To find the initial salary before the increase, we need to work backwards.
Let's set up the equation using the 5% increase information:
y = 1.05x --- (1)
We also know that there was a $2000 increase in the salary, so we can set up another equation:
y = x + 2000 --- (2)
We have a system of equations (equation 1 and equation 2) that we need to solve simultaneously to find the initial salary (x).
To solve these equations, we can substitute equation (2) into equation (1) because both equations represent the same value of y.
So, we substitute x + 2000 in place of y in equation (1):
x + 2000 = 1.05x
Now we can simplify and solve for x:
2000 = 1.05x - x
2000 = 0.05x
Dividing both sides by 0.05:
x = 2000 / 0.05
x = 40000
Therefore, the mayor's salary before the increase was $40,000.