Question

You want to buy the love of your life roses. If you make a bouquet of four red roses and eight white roses, the cost is $16.00. If you make a bouquet of six red roses and six white roses, the cost is $16.50. How much does each color of rose cost?

a) Red roses cost $2.00, white roses cost $1.00.
b) Red roses cost $1.50, white roses cost $2.00.
c) Red roses cost $1.00, white roses cost $2.50.
d) Red roses cost $2.50, white roses cost $1.00.

Answer 1

Red roses cost $1.375 and white roses cost $1.25.

Step-by-step explanation:

To determine the cost of each color of rose, we can set up a system of equations. Let x represent the cost of a red rose and y represent the cost of a white rose. From the given information, we can set up the following equations:

• 4x + 8y = 16.00
• 6x + 6y = 16.50

Simplifying the equations, we get:

• 2x + 4y = 8.00
• 6x + 6y = 16.50

Next, we can multiply the first equation by 3 to make the coefficients of x in both equations the same:

• 6x + 12y = 24.00
• 6x + 6y = 16.50

Subtracting the second equation from the first, we get:

• 6x + 12y - (6x + 6y) = 24.00 - 16.50
• 6x + 12y - 6x - 6y = 7.50
• 6y = 7.50
• y = 1.25

Substituting the value of y into the first equation, we get:

• 2x + 4(1.25) = 8.00
• 2x + 5 = 8.00
• 2x = 2.75
• x = 1.375

Therefore, red roses cost $1.375 and white roses cost $1.25.