The gardeners at middleton place gardens want to plant a total of 41 white and pink hydrangeas in one flower bed. in another flower bed, they want to plant 108 hydrangeas. in this bed, they want 2 times the number of white hydrangeas and 3 times the number of pink hydrangeas as in the first bed. use a system of equations to find how many white and how many pink hydrangeas the gardeners should buy altogether.

the gardeners should buy white hydrangeas and pink hydrangeas.

The gardeners should buy 45 white hydrangeas and 104 pink hydrangeas.

Step-by-step explanation:

Let the gardeners at Middleton Place Gardens have to buy x numbers of white hydrangeas and y number of pink hydrangeas.

So, x + y = 41 {Given} (1)

Again, for another flower bed they want to plant 108 hydrangeas, where the number of white ones is 2 times that of Middleton Place Gardens and the number of pink ones is 3 times that of Middleton Place Gardens.

So, 2x + 3y = 108 (2)

Now, solving equations (1) and (2) we get,

3y - 2y = 108 - 82 = 26

⇒ y = 26

And from equation (1) we get,

x = 41 - 26 = 15.

So, the total number of white hydrangeas the gardeners have to buy is (x + 2x) = 3x = 3 × 15 = 45.

And the total number of pink hydrangeas the gardeners have to buy is (y + 3y) = 4y = 4 × 26 = 104. (Answer)

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)