# Designer Flowers

### Boutique

## Situtation

Designer Flowers is a boutique that customizes flower bouquets. You want to buy a flower bouquet made of 20 flowers for your friend’s 20th birthday. When you went to the boutique and asked for the cost, they told you there is an initial cost for customizing and for the number of flowers used. The cost also varies according to if the order is placed on a week day or a weekend.

## Deals

**Week day: An initial cost of $15 for customizing and $2 per flower.**

** Weekend: An initial cost of $50 for customizing and $1.50 per flower. **

## When is is more economically reasonable to order a bouquet made of 20 flowers, week days or weekends?

Independent variable: Number of Flowers

Dependent variable: Total cost

**Week day: C=2f+15**

**Weekend: C=1.5f+50 **

__Standard form__

Week day: 2f-c+15=0

Weekend: 3f-2c+100=0

*C represents the total cost and f represents the number of flowers used*

## Find the Slope and y-intercept

m=dy/dx

X is the number of flowers

Y is the cost

__Week day __

dy: 35-15=20

The difference of y is 20

dx: 10-0=10

The difference of x is 10

The slope is 2

The y-intercept is 15 because it is the initial cost

__Weekend __

dy: 65-50=15

The difference of y is 15

dx: 10-0=10

The difference of x is 10

The slope is 1.5

The y-intercept is 50 because it is the initial cost

## Find the point of interception

__Find f__

C=2f+15

C=1.5f+50

2f+15=1.5f+50

2f-1.5f=50-15

0.5f=35

Divide both sides by 0.5

F=70

__Find C__

Substitute f to find C

C=2(70) +15

C= 140+15

C= 155

The coordinates for the point of interception are (70,155) since f is 70 and C is 155

## Significance

Ordering on a week day is more economical for less than 70 flowers. Ordering on a week day is less economical for more than 70 flowers. The point of interception is where the cost is the same, so the cost of ordering 70 flowers is the same on a week day or weekend.