Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Gordon is going to send some flowers to his wife. Dayton Florist charges $2 per rose, plus $11 for the vase. Cindy's Flowers, in contrast, charges $1 per rose and $35 for the vase. If Gordon 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? How many roses would there be? The cost will be $ if the bouquet contains roses.

Answer 1

Let's first set up the system of equations:

Let x be the number of roses in the bouquet.

For Dayton Florist:
2x + 11 = total cost

For Cindy's Flowers:
x + 35 = total cost

Since the cost is the same at both flower shops, we can set the two equations equal to each other:

2x + 11 = x + 35

Now we can solve for x:

2x - x = 35 - 11
x = 24

So, the cost will be $35 if the bouquet contains 24 roses.