# Smart Nails vs. Polish'd

### Who offers the better deal?

Bianca and Amaya want to get their nails done for the school dance coming up. They're on a strict budget so they have to find a good deal. They looked at 2 of their favourite nails salons in the G.T.A, "Smart Nails" and "Polish'd". At “Smart Nails” you can get a manicure for $30 plus $2 for a design per nail. At “Polish’d” you can get a manicure for $25 plus $3 for a design per nail. Which is a better deal if Amaya wants a manicure + design on 2 nails and if Bianca wants a manicure + designs on all 10 of her nails?

## Variables

## Equations

Polish'd: y+3x+25

## How to find the Point of Intersection

2x+30 = 3x+25

30-25 = 3x-2x

5 = x

Now that you've found the value of x. Replace it with x in both equations to find the value of y. They should be the same.

Smart Nails:

y=2x+30

y=2(5)+30

y=10+30

y=40

Polish'd:

y=3x+25

y=3(5)+25

y=15+25

y=40

so x= 5 and y=40 and the point of intersection is (5,40)