# Nails, Nails, Nails

## Snazzy Nails has the cheapest prices!!!

We simply stick to what we do best - creating beautiful nail designs and shaping those hands and feet. Come to Snazzy Nails the most luxurious nail salon and no longer will you have to be rich and famous to be treated like you are. Enjoy the luxury of your own personal spa-like while treating yourself to a magnificent manicure, and/or the perfect pedicure . We offer a unique nail care experience that relaxes you, relieves stress, improves well being and fits into your schedule and budget.

## Variables

Lets say x is number of hours.

Then y is the amount of money you will be paying/spending.

## Snazzy nails prices!!!

Equation of Line

Slope and y intercept form:

y=mx+b

y=7x+5

Standard form:

Ax + Bx + C = 0

0=7x-y+5

## Leading Nail Care Provider.

Equation of Line

Slope and y intercept form:

y=mx+b

y=5x+10

Standard form:

Ax + Bx + C = 0

0=5x-y+10

## Solution - Solving for a Point of Intersection

To find out when the two salons will charge the same number of products sold, we must solve the linear system, which is essentially finding a point of intersection.

1. We can solve by graphing

Using the equations given for each line, we can graph each line using the y intercept and rise over run for slope.

Snazzy Nails Salon

y = mx+b

y=7x+5

+5 is the y intercept so plot it

- Then use rise over run to graph the slope which is 7

- Graph the line

Leading Nail Care Provider

y = 5x + 10

- Repeat same steps

Then, using the 2 graphed lines, find the point of intersection. On the graph, the point of intersection is 2.5 hours spent on the nails which will result in you paying \$22.5.

2. You can also solve these linear systems by substitution (algebraically)

y = 5x + 10

y = 7x + 5

Sub in one equation into the other and solve for x

7x + 5 = 5x + 10

2x+5 = 10

2x = 5

x= 5/2

x = 2.5

Now sub x back into any equation and solve for y

y = 7(2.5) + 5

y = 22.8

Therefore, the point of intersection is (2.5 , 22.5)

## Snazzy Nail's Prices Compared to The Leading Nail Care Provider.

Legend

red line- leading nail care provider's prices

blue line- Snazzy nail's prices

## Conclusion

Snazzy nails is cheaper until 2.5 hours (where the break even point is).

The break even point is (POI) \$22.5 and 2.5 hours (2.5,22.5).

So at 2.5 hours both salons will charge you \$22.5.

After the break even point the leading nail care provider is cheaper.