Answer:
Both companies should sell 80 roses to charge the same
Step-by-step explanation:
Crossing of Lines
When two lines are drawn and they are not parallel, the cross at a certain point P(a,b). That point is the solution to the system of equations modeled by them.
Rose-R-Red sells its roses for a fixed down payment of $20 and an additional charge of $0.75 per stem. If x is the number of items sold by them then the charge is
[tex]\displaystyle c_1=20+0.75x[/tex]
The Flower Power sells its roses for a fixed down payment of $60 and an additional charge of $0.50 per stem. The function for their charge is
[tex]\displaystyle c_2=60+0.50x[/tex]
To know the number of roses for which both companies charges will be the same, we set
[tex]\displaystyle c_1=c_2[/tex]
Or equivalently
[tex]\displaystyle 20+0.75x=60+0.50x[/tex]
[tex]\displaystyle 0.25x=60-40[/tex]
[tex]\displaystyle x=\frac{20}{0.25}[/tex]
[tex]\boxed{\displaystyle x=80}[/tex]
So both companies should sell 80 roses to charge the same
