Question

Brad is going to send some flowers to his wife. Silvergrove Florist charges $3 per rose, plus $20 for the vase. Noah's Flowers, in contrast, charges $1 per rose and $30 for the vase. If Brad orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be?Write a system of equations, graph them, and type the solution.

Answer 1

To solve this exercise we must first identify our variables

• C, = Total cost

,

• r ,= number of roses

,

• v ,= number of vases

Now, with these variables we will formulate the equations that model the price of each of the flower shops. We have to take into account that Brad is only going to buy one vase

`v=1`

Silvergroce Florist

`\begin{gathered} C=3r+20v \\ C=3r+20(1) \\ C=3r+20\to(1) \end{gathered}`

Noah's Flowers

`\begin{gathered} C=1r+30v \\ C=r+30(1) \\ C=r+30\to(2) \end{gathered}`

We have two equations (1) and (2), to find the total cost that is the same in both flower shops, we only have to equal them to find the number of roses that Brad should buy

`\begin{gathered} 3r+20=r+30 \\ 3r-r=30-20 \\ 2r=10 \\ r=(10)/(2) \\ r=5 \end{gathered}`

Brad must buy 5 roses so that it costs the same at both florists. To know the cost we substitute in any equation (1) or (2) the number of roses

`\begin{gathered} C=r+30 \\ C=5+30 \\ C=35 \end{gathered}`
`\begin{gathered} C=3r+20 \\ C=3(5)+20 \\ C=15+20 \\ C=35 \end{gathered}`

The total cost for 5 roses and a vase is $35

Answer 2

y = 20 + 3x

y = 30+x

( 5,35)

Explanation:

Writing and solving a system of equations

Silvergrove Florist: 20 + 3x

Noah's Flowers: 30 + 1x where x is the number of roses

We want to know when they are equal

20+3x = 30+1x

Subtract x from each side

20+3x-x = 30+x-x

20+2x = 30

Subtract 20 from each side

20+2x-20 = 30-20

2x = 10

Divide by 2

2x/2 = 10/2

x = 5

The number of roses is 5

The cost is

30 +x = 30+5 = 35

(5,35)