Question

Roses cost $2.50 each and daises cost $1.75 each. Sam spent $24.75 to buy a dozen flowers for his mother. The bouquet contained both roses and daises. How many of each type of flower were in the bouquet?

Answer 1

To find the number of roses and daisies in the bouquet, we can set up a system of equations based on the given information. From the problem, the cost of a rose is $2.50 and the cost of a daisy is $1.75. Sam spent a total of $24.75 on the bouquet and there are 12 flowers in total. By solving the system of equations, we can determine that there are 5 roses and 7 daisies in the bouquet.

Step-by-step explanation:

To find the number of roses and daisies in the bouquet, we can set up a system of equations based on the given information. Let's assume there are x roses and y daisies in the bouquet:

From the problem, we know that the cost of a rose is $2.50 and the cost of a daisy is $1.75. We also know that Sam spent a total of $24.75 on the bouquet, and there are 12 flowers in total.

So we can set up the following equations:

• x + y = 12 (equation 1)
• 2.50x + 1.75y = 24.75 (equation 2)

We can solve this system of equations by substitution or elimination. I will use substitution:

1. Solve equation 1 for x: x = 12 - y
2. Substitute the value of x in equation 2: 2.50(12 - y) + 1.75y = 24.75
3. Simplify and solve for y: 30 - 2.50y + 1.75y = 24.75
4. Combine like terms: -0.75y = -5.25
5. Divide by -0.75: y = 7

Now we know that there are 7 daisies in the bouquet. We can substitute this value back into equation 1 to find the number of roses: x + 7 = 12, so x = 5

Therefore, there are 5 roses and 7 daisies in the bouquet.

Answer 2

Answer:The equation for the flowers Sam can purchase for his mother is 2.5x + 1.75y < 24.75. There are many acceptable answers for this, such as buying only 1 to 9 roses. If Sam wants to spend all of his $24.75 budget, he can get 5 roses and 7 daisies for a bouquet: 5*$2.50 = $12.50, 7*$1.75= $12.25, $12.50+$12.25 = $24.75

Step-by-step explanation: