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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Kirk is going to send some flowers to his wife. Lakeside Florist charges per rose, plus for the vase. Colette's Flowers, in contrast, charges per rose and for the vase. If Kirk orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. How many roses would there be? What would the total cost be?If the bouquet contains roses, it will cost .
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Kirk is going to send some flowers to his wife. Lakeside Florist charges per rose, plus for the vase. Colette's Flowers, in contrast, charges per rose and for the vase. If Kirk orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. How many roses would there be? What would the total cost be?If the bouquet contains roses, it will cost .
- Set up equations: Set up the equations based on the given information.Lakeside Florist: Cost = per rose + for the vase.Colette's Flowers: Cost = per rose + for the vase.Since the cost is the same for both, we can write the equations as:Let's denote the number of roses as ''.
- Write system: Write the system of equations.Lakeside Florist: Colette's Flowers: Since the costs are equal, we have:
- Solve equations: Solve the system of equations.Subtract from both sides to get the roses on one side:Now, subtract from both sides to solve for :
- Find total cost: Find the total cost.Now that we know the number of roses is , we can plug this into either florist's cost equation to find the total cost. Let's use Lakeside Florist's equation:Cost Cost Cost
- Verify solution: Verify the solution with Colette's Flowers' cost equation.Cost = Cost = Cost = Since the cost is the same for both florists, our solution is correct.
