Tony is making flower arrangements. He is using 3 different kinds of flowers--roses, daisies, and tulips. Each arrangement will have the same number of each kind of flower. He figures that if he uses all the flowers, the greatest number of arrangements he can make is 7. He has 42 flowers in all, with more daisies than tulips, and more tulips than roses. How many of each kind of flower does Tony have?

Question

Tony is making flower arrangements. He is using 3 different kinds of flowers--roses, daisies, and tulips. Each arrangement will have the same number of each kind of flower. He figures that if he uses all the flowers, the greatest number of arrangements he can make is 7. He has 42 flowers in all, with more daisies than tulips, and more tulips than roses. How many of each kind of flower does Tony have?

Answer 1

42 flowers in 7 arrangements means 6 flowers per arrangement.

d > t
t > r

1+2+3 = 6

so, there must be 1 rose, 2 tulips, 3 daisies in each arrangement.

multiply by 7 for all the arrangements.

Answer 2

To solve this problem, we can set up a system of equations based on the given information. Let's denote the number of roses as R, the number of daisies as D, and the number of tulips as T.

According to the problem, each arrangement will have the same number of each kind of flower. So, we can assume that the number of each type of flower will be a factor of the total number of flowers.

We are told that the greatest number of arrangements Tony can make is 7. Since each arrangement will use the same number of each kind of flower, the total number of flowers must also be a multiple of 7.

We are also given that Tony has a total of 42 flowers. So, we can write the following equation:

R + D + T = 42

Since there are more daisies than tulips and more tulips than roses, we can set up the following inequalities:

D > T
T > R

Now, let's try to find the possible values for R, D, and T.

Since the total number of flowers must be a multiple of 7, let's try different values for R, D, and T that satisfy this condition:

If we start with R = 1, D = 8, and T = 14, we have a total of 1 + 8 + 14 = 23 flowers. This is not a multiple of 7.

If we try R = 2, D = 9, and T = 14, we have a total of 2 + 9 + 14 = 25 flowers. Again, this is not a multiple of 7.

By trying different values, we find that the values R = 3, D = 10, and T = 14 satisfy all the given conditions. This adds up to a total of 3 + 10 + 14 = 27 flowers, which is a multiple of 7.

Therefore, Tony has 3 roses, 10 daisies, and 14 tulips.