Question

Rose-R-Red has offered to sell its roses for a fixed down payment of 20 and an additional charge of 0.75 per stem. the Flower Power has offered to sell its roses for a fixed down payment of 60 and an additional charge of 0.50 per stem Find the number of roses for which the companies charges will be the same

Answer 1

Both companies should sell 80 roses to charge the same

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

`\displaystyle c_1=20+0.75x`

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

`\displaystyle c_2=60+0.50x`

To know the number of roses for which both companies charges will be the same, we set

`\displaystyle c_1=c_2`

Or equivalently

`\displaystyle 20+0.75x=60+0.50x`

`\displaystyle 0.25x=60-40`

`\displaystyle x=(20)/(0.25)`

`\boxed{\displaystyle x=80}`

So both companies should sell 80 roses to charge the same