# Publication Companies' Charges

### A Linear System

## A Linear System Explanation

Two online suppliers of printed and promotional materials and marketing provide services to consumers. The two online suppliers are VistaPrint and Herrschners. Vistaprint is a new and improved service in Brampton, whereas Herrschners is an old, yet helpful service in Brampton. VistaPrint and Herrschners are given contracts to print out 50 holiday cards. VistaPrint charges $18.00 for the design of the holiday card. There is an additional charge of $1.25 per holiday card printed. Herrschners charges $4 dollars per holiday card printed.

## Identifying the Variables

C=Cost

V=VistaPrint number of Cards

H=Herrschners number of Cards

## The Solution

## Specified Equations for each Companies' Charges

Vistaprint Charges:

Equation In the form y=mx+b

Y= 1.25x+18

-1.25x-y-18=0

Herrschners Charges:

Equation in the form y=mx

Y= 4x

-4x-y=0

## VistaPrint Charges for an (x) amount of Cards

## Herreschners Charges for an (x) amount of Cards

## Significance of the Solution of this Linear System

The solution to the problem is to first graph both of the values; Herrschners Charges and VistaPrint Charges. Using the graph you can extrapolate and visualize the solution. However, you can use the equations for both values and substitute (x) and (y) and solve the equation. For example:

Vistaprint Charges an (y) amount for 50 cards

Y amount:

Y=mx+b

Y= 1.25x+18

X= The number of cards

Since y=1.25x+18, (x) can be substituted as 50

So,

Y=1.25x+18

Y=1.25x50+18

Y= 62.5+18

Y=80.5

Vistaprint charges $80.5 for 50 holiday cards

Herrschners Charges an (y) amount for 50 cards

Y amount:

Y=mx

Y=4x

X= The number of cards

Since y=4x, (x) can be substitute as 50

So,

Y=4x

Y=4x

Y=4x50

Y=200

Herrschners charges $200 for 50 holiday cards.

## Graphic Solution

## Summary Statement

The two companies' intersect at; 6.5,26.13

This intersecting point shows that 6.5 cards for both companies will cost the same, $26.13