Question

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.

Answer 1

The gardeners should buy 10 white hydrangeas and 93 pink hydrangeas.

Step-by-step explanation:

Let's define:

• x = number of white hydrangeas in the first flower bed
• y = number of pink hydrangeas in the first flower bed
• w = number of white hydrangeas in the second flower bed
• p = number of pink hydrangeas in the second flower bed

We can set up the following system of equations:

1. x + y = 41
2. w + p = 108
3. w = 2x
4. p = 3y

Solving the system of equations, we find:

• x = 10
• y = 31
• w = 20
• p = 93

Therefore, the gardeners should buy 10 white hydrangeas and 93 pink hydrangeas.

Answer 2

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)