Answer :
a) Given in the question that the hiring bonus is one time that is fixed. In the equation y = 200 + 115x
We see that 200 is constant and is independent of influence of any variables. So the hiring bonus is 200
b) We can interpret from the equation y = 200 + 115x that, 115 is the pay per hour because x is the total number of hours worked and we need to multiply the total number of hours with a quantity per hour to maintain the homogeneity of the equation. As y is the total pay, so we need to multiply pay per hour to x by the laws of homogeneity. Therefore 115 must be the pay per hour in order to balance with x. Hence the hourly wage is 115 per hour.
Given: New employees receive a time pay bonus. The equation y = 200 + 115x, gives a new total pay y, for x working hours.
What are algebraic expressions?
Algebraic expressions are the sequences or combinations of characters containing letters, numbers, variables, symbols, etc. The algebraic expressions help us to form an equation for a given large problem, thus making it short and easy to understand.
We can form algebraic equations for every problem with the help of variables.
Algebraic expressions also help us to formulate graphs and analyze the problem with a large number of values for the independent and dependent variables.
What is the equation of a straight line?
The equation of straight line is y = mx + c, where c is the intercept in the y axis where the line passes from and m is the slope of the line.
Now, let's solve the given question.
The given equation is:
y = 200 + 115x
where y = Total pay for the employee
and x = Total working hours
a) Given in the question that the hiring bonus is one time that is fixed. In the equation y = 200 + 115x
We see that 200 is constant and is independent of influence of any variables. So the hiring bonus is 200
b) We can interpret from the equation y = 200 + 115x that, 115 is the pay per hour because x is the total number of hours worked and we need to multiply the total number of hours with a quantity per hour to maintain the homogeneity of the equation. As y is the total pay, so we need to multiply pay per hour to x by the laws of homogeneity. Therefore 115 must be the pay per hour in order to balance with x. Hence the employees are paid 115 per hour.
Hence the hiring bonus is 200 and the pay per hour or hourly wage is 115 per hour.
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Disclaimer: The given question is incomplete. The complete question is given below:
A local restaurant is trying to recruit new employees. As an incentive to work there, they are offering a hiring bonus. In addition to
their hourly wages, new employees will receive a one-time pay bonus. The equation y = 200 + 115x gives a new employees total
pay, y, for working x hours.
a. How much is the hiring bonus? Explain.
b. How much does the employee get paid as their hourly wage? explain
