Question

1. a flower shop sells two types of bouquets. bouquet a consists of a dozen roses and some carnations. bouquet b consists of a dozen peonies and some lilies. the price of one dozen peonies is 3 times the price of one dozen roses, as shown in the table. the cost of five bouquets a is the same as the cost of two bouquets b. what is the cost of a dozen roses?

Explanation:

Step1: Find the cost expressions for Bouquet A and Bouquet B

• Bouquet A: Let the cost of a dozen roses be \(x\). The cost of Bouquet A is \(x + 7\) (a dozen roses \(x\) + a dozen lilies \(7\)).
• Bouquet B: The cost of a dozen peonies is \(3x\). The cost of Bouquet B is \(3x+5\) (a dozen peonies \(3x\)+ a dozen carnations \(5\)).

Step2: Set up the equation based on the cost relationship

• Given that the cost of five Bouquets A is the same as the cost of two Bouquets B.
• The cost of five Bouquets A is \(5(x + 7)\).
• The cost of two Bouquets B is \(2(3x + 5)\).
• So, the equation is \(5(x + 7)=2(3x + 5)\).

Step3: Solve the equation

• Expand both sides:
• \(5x+35 = 6x + 10\).
• Subtract \(5x\) from both sides:
• \(35=6x + 10-5x\).
• Simplify:
• \(35=x + 10\).
• Subtract \(10\) from both sides:
• \(x=35 - 10\).
• \(x = 25\).

Answer:

\(25\)