Linear Modeling
Some situations in life can be mathematically modeled as lines. The equation of a line in slope-intercept form is:
y = mx + b
Where x and y are the independent and dependent variables respectively, and m and b are constants.
Here we are dealing with a situation where the dependent variable is called P, the total of Jake's weekly pay in a week.
1) We are told that the total payment depends on the total sales on a 5.75% commission and a fixed amount of $130.
If we call T to the total sales, then the variable part of Jake's payment is 0.0575T. Recall we must divide by 100 any number given in %.
The linear equation that models the payment for Jake is:
P = 0.0575T + 130
2) We can use the model above to find the value of T, knowing that Jake was paid $604.95 for a week. We need to solve the equation:
604.95 = 0.0575T + 130
Subtracting 130:
604.95 - 130 = 0.0575T = 474.95
Dividing by 0.0575:
T = 474.95 / 0.0575
T = $8260
That week's total sales were $8260