Question

Andrea rents a chair at a hair salon. When she has given 12 haircuts in a month, she makes $285. When she has given 26 haircuts in a month, she makes $1055. Write an equation expressing the number of haircuts and Andrea's income:

Answer 1

To find the equation expressing Andrea's income from her haircuts, we calculate the slope (price per haircut) and the y-intercept (initial fee). The resulting equation is y = $55x - $375, where y is the income and x is the number of haircuts.

Step-by-step explanation:

We need to establish a linear relationship between the number of haircuts Andrea gives and her income. Using the information provided, we observe that Andrea's income changes with the number of haircuts, which suggests a linear equation of the form y = mx + b, where y represents the total income, x represents the number of haircuts, m represents the additional money made per haircut, and b represents the base charge or initial fee.

From the given data points (12, $285) and (26, $1055), we can find m by calculating the slope:

m = (Income2 - Income1) / (Haircuts2 - Haircuts1) = ($1055 - $285) / (26 - 12) = $770 / 14 = $55

Thus, Andrea earns $55 per haircut. To find b, we can substitute one of the points into the equation:

$285 = 12($55) + b

b = $285 - 12($55) = $285 - $660 = -$375

Now, we can write the final equation that expresses Andrea's income in terms of the number of haircuts given:

y = $55x - $375