Final answer:
Andrea needs to give approximately 43 haircuts in a month to make $2000, based on the linear equation derived from the earnings provided at 12 and 26 haircuts.
Step-by-step explanation:
To solve how many haircuts Andrea needs to give to make $2000 a month, let's use the two points provided (12 haircuts for $285, and 26 haircuts for $1055) to find a linear equation that will represent Andrea's earnings based on the number of haircuts given. We can use the slope-intercept form (y = mx + b) for this linear equation, where y represents the total earnings, x the number of haircuts, m the slope (amount Andrea earns per haircut), and b is the y-intercept (Andrea's fixed costs or baseline earnings).
First, let's calculate the slope m, which is change in earnings divided by change in haircuts: m = (1055 - 285) / (26 - 12) = 770 / 14 = 55. This means Andrea earns $55 per haircut. Next, we'll find the y-intercept b using one of the points, let's use (12, 285):
285 = 55(12) + b, which simplifies to
285 = 660 + b, and solving for b gives us
b = 285 - 660, so
b = -375.
The full equation is y = 55x - 375.
Finally, to find out how many haircuts are needed to make $2000, we'll set y to $2000 and solve for x:
2000 = 55x - 375,
which simplifies to
2375 = 55x, and dividing both sides by 55 gives us
x ≈ 43.18.
Therefore, Andrea has to give approximately 43 haircuts in a month to make $2000.